How to graph a line - PSAT Math
Card 1 of 42
The equation 
represents a line. This line does NOT pass through which of the four quadrants?
The equation
Tap to reveal answer
Plug in 
for 
to find a point on the line:
Thus, 
is a point on the line.
Plug in 
for 
to find a second point on the line:
is another point on the line.
Now we know that the line passes through the points 
and 
.
A quick sketch of the two points reveals that the line passes through all but the third quadrant.
Plug in
Thus,
Plug in
Now we know that the line passes through the points
A quick sketch of the two points reveals that the line passes through all but the third quadrant.
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A line graphed on the coordinate plane below. 
Give the equation of the line in slope intercept form.
A line graphed on the coordinate plane below.
Give the equation of the line in slope intercept form.
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The slope of the line is 
and the y-intercept is 
.
The equation of the line is 
.
The slope of the line is
The equation of the line is
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Give the equation of the curve.
Give the equation of the curve.
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This is the parent graph of 
. Since the graph in question is negative, then we flip the quadrants in which it will approach infinity. So the graph of 
will start in quadrant 2 and end in 4.
This is the parent graph of
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What is the equation of the line in the graph above?
What is the equation of the line in the graph above?
Tap to reveal answer
In order to find the equation of a line in slope-intercept form 
, where 
is the slope and 
is the y-intercept), one must know or otherwise figure out the slope of the line (its rate of change) and the point at which it intersects the y-axis. By looking at the graph, you can see that the line crosses the y-axis at 
. Therefore, 
.
Slope is the rate of change of a line, which can be calculated by figuring out the change in y divided by the change in x, using the formula
.
When looking at a graph, you can pick two points on a graph and substitute their x- and y-values into that equation. On this graph, it's easier to choose points like 
and 
. Plug them into the equation, and you get
Plugging in those values for 
and 
in the equation, and you get 
In order to find the equation of a line in slope-intercept form
Slope is the rate of change of a line, which can be calculated by figuring out the change in y divided by the change in x, using the formula
When looking at a graph, you can pick two points on a graph and substitute their x- and y-values into that equation. On this graph, it's easier to choose points like
Plugging in those values for
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What are the x- and y- intercepts of the equation 
?
What are the x- and y- intercepts of the equation
Tap to reveal answer
Answer: (1/2,0) and (0,-2)
Finding the y-intercept: The y-intercept is the point at which the line crosses tye y-axis, meaning that x = 0 and the format of the ordered pair is (0,y) with y being the y-intercept. The equation 
is in slope-intercept (
) form, meaning that the y-intercept, b, is actually given in the equation. b = -2, which means that our y-intercept is -2. The ordered pair for expressing this is (0,-2)
Finding the x-intercept: To find the x-intercept of the equation 
, we must find the point where the line of the equation crosses the x-axis. In other words, we must find the point on the line where y is equal to 0, as it is when crossing the x-axis. Therefore, substitute 0 into the equation and solve for x: 
The x-interecept is therefore (1/2,0).
Answer: (1/2,0) and (0,-2)
Finding the y-intercept: The y-intercept is the point at which the line crosses tye y-axis, meaning that x = 0 and the format of the ordered pair is (0,y) with y being the y-intercept. The equation
Finding the x-intercept: To find the x-intercept of the equation
The x-interecept is therefore (1/2,0).
← Didn't Know|Knew It →
Which of the following could be the equation of the line shown in this graph?
Which of the following could be the equation of the line shown in this graph?
Tap to reveal answer
The line in the diagram has a negative slope and a positive y-intercept. It has a negative slope because the line moves from the upper left to the lower right, and it has a positive y-intercept because the line intercepts the y-axis above zero.
The only answer choice with a negative slope and a positive y-intercept is
The line in the diagram has a negative slope and a positive y-intercept. It has a negative slope because the line moves from the upper left to the lower right, and it has a positive y-intercept because the line intercepts the y-axis above zero.
The only answer choice with a negative slope and a positive y-intercept is
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The equation represents a line. This line does NOT pass through which of the four quadrants?
The equation
Tap to reveal answer
Plug in for to find a point on the line:
Thus, is a point on the line.
Plug in for to find a second point on the line:
is another point on the line.
Now we know that the line passes through the points and .
A quick sketch of the two points reveals that the line passes through all but the third quadrant.
Plug in
Thus,
Plug in
Now we know that the line passes through the points
A quick sketch of the two points reveals that the line passes through all but the third quadrant.
← Didn't Know|Knew It →
A line graphed on the coordinate plane below.
Give the equation of the line in slope intercept form.
A line graphed on the coordinate plane below.
Give the equation of the line in slope intercept form.
Tap to reveal answer
The slope of the line is and the y-intercept is .
The equation of the line is .
The slope of the line is
The equation of the line is
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Give the equation of the curve.
Give the equation of the curve.
Tap to reveal answer
This is the parent graph of . Since the graph in question is negative, then we flip the quadrants in which it will approach infinity. So the graph of will start in quadrant 2 and end in 4.
This is the parent graph of
← Didn't Know|Knew It →
What is the equation of the line in the graph above?
What is the equation of the line in the graph above?
Tap to reveal answer
In order to find the equation of a line in slope-intercept form , where is the slope and is the y-intercept), one must know or otherwise figure out the slope of the line (its rate of change) and the point at which it intersects the y-axis. By looking at the graph, you can see that the line crosses the y-axis at . Therefore, .
Slope is the rate of change of a line, which can be calculated by figuring out the change in y divided by the change in x, using the formula
.
When looking at a graph, you can pick two points on a graph and substitute their x- and y-values into that equation. On this graph, it's easier to choose points like and . Plug them into the equation, and you get
Plugging in those values for and in the equation, and you get
In order to find the equation of a line in slope-intercept form
Slope is the rate of change of a line, which can be calculated by figuring out the change in y divided by the change in x, using the formula
When looking at a graph, you can pick two points on a graph and substitute their x- and y-values into that equation. On this graph, it's easier to choose points like
Plugging in those values for
← Didn't Know|Knew It →
What are the x- and y- intercepts of the equation ?
What are the x- and y- intercepts of the equation
Tap to reveal answer
Answer: (1/2,0) and (0,-2)
Finding the y-intercept: The y-intercept is the point at which the line crosses tye y-axis, meaning that x = 0 and the format of the ordered pair is (0,y) with y being the y-intercept. The equation is in slope-intercept () form, meaning that the y-intercept, b, is actually given in the equation. b = -2, which means that our y-intercept is -2. The ordered pair for expressing this is (0,-2)
Finding the x-intercept: To find the x-intercept of the equation , we must find the point where the line of the equation crosses the x-axis. In other words, we must find the point on the line where y is equal to 0, as it is when crossing the x-axis. Therefore, substitute 0 into the equation and solve for x:
The x-interecept is therefore (1/2,0).
Answer: (1/2,0) and (0,-2)
Finding the y-intercept: The y-intercept is the point at which the line crosses tye y-axis, meaning that x = 0 and the format of the ordered pair is (0,y) with y being the y-intercept. The equation
Finding the x-intercept: To find the x-intercept of the equation
The x-interecept is therefore (1/2,0).
← Didn't Know|Knew It →
Which of the following could be the equation of the line shown in this graph?
Which of the following could be the equation of the line shown in this graph?
Tap to reveal answer
The line in the diagram has a negative slope and a positive y-intercept. It has a negative slope because the line moves from the upper left to the lower right, and it has a positive y-intercept because the line intercepts the y-axis above zero.
The only answer choice with a negative slope and a positive y-intercept is
The line in the diagram has a negative slope and a positive y-intercept. It has a negative slope because the line moves from the upper left to the lower right, and it has a positive y-intercept because the line intercepts the y-axis above zero.
The only answer choice with a negative slope and a positive y-intercept is
← Didn't Know|Knew It →
The equation represents a line. This line does NOT pass through which of the four quadrants?
The equation
Tap to reveal answer
Plug in for to find a point on the line:
Thus, is a point on the line.
Plug in for to find a second point on the line:
is another point on the line.
Now we know that the line passes through the points and .
A quick sketch of the two points reveals that the line passes through all but the third quadrant.
Plug in
Thus,
Plug in
Now we know that the line passes through the points
A quick sketch of the two points reveals that the line passes through all but the third quadrant.
← Didn't Know|Knew It →
A line graphed on the coordinate plane below.
Give the equation of the line in slope intercept form.
A line graphed on the coordinate plane below.
Give the equation of the line in slope intercept form.
Tap to reveal answer
The slope of the line is and the y-intercept is .
The equation of the line is .
The slope of the line is
The equation of the line is
← Didn't Know|Knew It →
Give the equation of the curve.
Give the equation of the curve.
Tap to reveal answer
This is the parent graph of . Since the graph in question is negative, then we flip the quadrants in which it will approach infinity. So the graph of will start in quadrant 2 and end in 4.
This is the parent graph of
← Didn't Know|Knew It →
What is the equation of the line in the graph above?
What is the equation of the line in the graph above?
Tap to reveal answer
In order to find the equation of a line in slope-intercept form , where is the slope and is the y-intercept), one must know or otherwise figure out the slope of the line (its rate of change) and the point at which it intersects the y-axis. By looking at the graph, you can see that the line crosses the y-axis at . Therefore, .
Slope is the rate of change of a line, which can be calculated by figuring out the change in y divided by the change in x, using the formula
.
When looking at a graph, you can pick two points on a graph and substitute their x- and y-values into that equation. On this graph, it's easier to choose points like and . Plug them into the equation, and you get
Plugging in those values for and in the equation, and you get
In order to find the equation of a line in slope-intercept form
Slope is the rate of change of a line, which can be calculated by figuring out the change in y divided by the change in x, using the formula
When looking at a graph, you can pick two points on a graph and substitute their x- and y-values into that equation. On this graph, it's easier to choose points like
Plugging in those values for
← Didn't Know|Knew It →
What are the x- and y- intercepts of the equation ?
What are the x- and y- intercepts of the equation
Tap to reveal answer
Answer: (1/2,0) and (0,-2)
Finding the y-intercept: The y-intercept is the point at which the line crosses tye y-axis, meaning that x = 0 and the format of the ordered pair is (0,y) with y being the y-intercept. The equation is in slope-intercept () form, meaning that the y-intercept, b, is actually given in the equation. b = -2, which means that our y-intercept is -2. The ordered pair for expressing this is (0,-2)
Finding the x-intercept: To find the x-intercept of the equation , we must find the point where the line of the equation crosses the x-axis. In other words, we must find the point on the line where y is equal to 0, as it is when crossing the x-axis. Therefore, substitute 0 into the equation and solve for x:
The x-interecept is therefore (1/2,0).
Answer: (1/2,0) and (0,-2)
Finding the y-intercept: The y-intercept is the point at which the line crosses tye y-axis, meaning that x = 0 and the format of the ordered pair is (0,y) with y being the y-intercept. The equation
Finding the x-intercept: To find the x-intercept of the equation
The x-interecept is therefore (1/2,0).
← Didn't Know|Knew It →
Which of the following could be the equation of the line shown in this graph?
Which of the following could be the equation of the line shown in this graph?
Tap to reveal answer
The line in the diagram has a negative slope and a positive y-intercept. It has a negative slope because the line moves from the upper left to the lower right, and it has a positive y-intercept because the line intercepts the y-axis above zero.
The only answer choice with a negative slope and a positive y-intercept is
The line in the diagram has a negative slope and a positive y-intercept. It has a negative slope because the line moves from the upper left to the lower right, and it has a positive y-intercept because the line intercepts the y-axis above zero.
The only answer choice with a negative slope and a positive y-intercept is
← Didn't Know|Knew It →
What are the x- and y- intercepts of the equation ?
What are the x- and y- intercepts of the equation
Tap to reveal answer
Answer: (1/2,0) and (0,-2)
Finding the y-intercept: The y-intercept is the point at which the line crosses tye y-axis, meaning that x = 0 and the format of the ordered pair is (0,y) with y being the y-intercept. The equation is in slope-intercept () form, meaning that the y-intercept, b, is actually given in the equation. b = -2, which means that our y-intercept is -2. The ordered pair for expressing this is (0,-2)
Finding the x-intercept: To find the x-intercept of the equation , we must find the point where the line of the equation crosses the x-axis. In other words, we must find the point on the line where y is equal to 0, as it is when crossing the x-axis. Therefore, substitute 0 into the equation and solve for x:
The x-interecept is therefore (1/2,0).
Answer: (1/2,0) and (0,-2)
Finding the y-intercept: The y-intercept is the point at which the line crosses tye y-axis, meaning that x = 0 and the format of the ordered pair is (0,y) with y being the y-intercept. The equation
Finding the x-intercept: To find the x-intercept of the equation
The x-interecept is therefore (1/2,0).
← Didn't Know|Knew It →
The equation represents a line. This line does NOT pass through which of the four quadrants?
The equation
Tap to reveal answer
Plug in for to find a point on the line:
Thus, is a point on the line.
Plug in for to find a second point on the line:
is another point on the line.
Now we know that the line passes through the points and .
A quick sketch of the two points reveals that the line passes through all but the third quadrant.
Plug in
Thus,
Plug in
Now we know that the line passes through the points
A quick sketch of the two points reveals that the line passes through all but the third quadrant.
← Didn't Know|Knew It →