Slope - SSAT Upper Level: Quantitative

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Question

What is the slope of the line that passes through the points $(-1,4) \text{ and } (-5,1)$ ?

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Answer

Use the following formula to find the slope:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

Substituting the values from the points given, we get the following slope:

$\text{Slope}=\frac{1-4}{-5-(-1)}=\frac{-3}{-4}=\frac{3}{4}$

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Question

Find the slope of a line that passes through the points and .

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Answer

To find the slope of the line that passes through the given points, you can use the slope equation.

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\text{Slope}=\frac{-1-2}{-2-17}=\frac{-3}{-19}=\frac{3}{19}$

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Question

Find the slope of the line that passes through the points and .

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Answer

To find the slope of the line that passes through the given points, you can use the slope equation.

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\text{Slope}=\frac{3-b}{2-a}$

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Question

What is the slope of the line with the equation

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Answer

To find the slope, put the equation in the form of .

$y=-\frac{2}{3}x-3$

Since $m=-\frac{2}{3}$ , that is the value of the slope.

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Question

A line has the equation . What is the slope of this line?

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Answer

You need to put the equation in form before you can easily find out its slope.

$y=\frac{5}{9}x-\frac{4}{3}$

Since $m=\frac{5}{9}$ , that must be the slope.

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Question

Find the slope of the line that goes through the points and .

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Answer

Even though there are variables involved in the coordinates of these points, you can still use the slope formula to figure out the slope of the line that connects them.

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\text{Slope}=\frac{-9s-8s}{2t-4t}=\frac{-17s}{-2t}=\frac{17s}{2t}$

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Question

The equation of a line is . Find the slope of this line.

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Answer

To find the slope, you will need to put the equation in form. The value of will be the slope.

Subtract from either side:

Divide each side by :

$y=\frac{3}{2}x-\frac{3}{4}$

You can now easily identify the value of .

$m=\frac{3}{2}$

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Question

Find the slope of the line that passes through the points and .

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Answer

You can use the slope formula to figure out the slope of the line that connects these two points. Just substitute the specified coordinates into the equation and then subtract:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\text{Slope}=\frac{3-1}{0-8}=\frac{2}{-8}=-\frac{1}{4}$

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Question

Find the slope of the following function:

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Answer

Rewrite the equation in slope-intercept form, .

$\frac{2x-3}{6}=y$

$y=\frac{1}{3}x-\frac{1}{2}$

The slope is the term, which is $\frac{1}{3}$ .

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Question

Find the slope of the line given the two points: $(5,8) \textup{ and } (-3,-7)$

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Answer

Write the formula to find the slope.

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{y_1-y_2}{x_1-x_2}$

Either equation will work. Let's choose the latter. Substitute the points.

$m=\frac{y_1-y_2}{x_1-x_2}=\frac{8-(-7)}{5-(-3)}= \frac{15}{8}$

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Question

Consider the line of the equation . The line of a function has the same slope as that of . Which of the following could be the definition of ?

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Answer

The definition of is written in slope-intercept form , in which , the coefficient of , is the slope of its line. , so the slope of its line is .

We must select the choice whose line has this slope. The definition of in each choice is also written in slope-intercept form, so we select the alternative with -coefficient 5; the only such alternative is .

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Question

What is the slope of the line that passes through the points $(-1,4) \text{ and } (-5,1)$ ?

Tap to reveal answer

Answer

Use the following formula to find the slope:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

Substituting the values from the points given, we get the following slope:

$\text{Slope}=\frac{1-4}{-5-(-1)}=\frac{-3}{-4}=\frac{3}{4}$

← Didn't Know|Knew It →

Question

Find the slope of a line that passes through the points and .

Tap to reveal answer

Answer

To find the slope of the line that passes through the given points, you can use the slope equation.

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\text{Slope}=\frac{-1-2}{-2-17}=\frac{-3}{-19}=\frac{3}{19}$

← Didn't Know|Knew It →

Question

Find the slope of the line that passes through the points and .

Tap to reveal answer

Answer

To find the slope of the line that passes through the given points, you can use the slope equation.

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\text{Slope}=\frac{3-b}{2-a}$

← Didn't Know|Knew It →

Question

What is the slope of the line with the equation

Tap to reveal answer

Answer

To find the slope, put the equation in the form of .

$y=-\frac{2}{3}x-3$

Since $m=-\frac{2}{3}$ , that is the value of the slope.

← Didn't Know|Knew It →

Question

A line has the equation . What is the slope of this line?

Tap to reveal answer

Answer

You need to put the equation in form before you can easily find out its slope.

$y=\frac{5}{9}x-\frac{4}{3}$

Since $m=\frac{5}{9}$ , that must be the slope.

← Didn't Know|Knew It →

Question

Find the slope of the line that goes through the points and .

Tap to reveal answer

Answer

Even though there are variables involved in the coordinates of these points, you can still use the slope formula to figure out the slope of the line that connects them.

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\text{Slope}=\frac{-9s-8s}{2t-4t}=\frac{-17s}{-2t}=\frac{17s}{2t}$

← Didn't Know|Knew It →

Question

The equation of a line is . Find the slope of this line.

Tap to reveal answer

Answer

To find the slope, you will need to put the equation in form. The value of will be the slope.

Subtract from either side:

Divide each side by :

$y=\frac{3}{2}x-\frac{3}{4}$

You can now easily identify the value of .

$m=\frac{3}{2}$

← Didn't Know|Knew It →

Question

Find the slope of the line that passes through the points and .

Tap to reveal answer

Answer

You can use the slope formula to figure out the slope of the line that connects these two points. Just substitute the specified coordinates into the equation and then subtract:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\text{Slope}=\frac{3-1}{0-8}=\frac{2}{-8}=-\frac{1}{4}$

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Question

Find the slope of the following function:

Tap to reveal answer

Answer

Rewrite the equation in slope-intercept form, .

$\frac{2x-3}{6}=y$

$y=\frac{1}{3}x-\frac{1}{2}$

The slope is the term, which is $\frac{1}{3}$ .

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