Vertical and Horizontal Lines - Algebra 2

Slope is defined as rise over run. So a slope of .7 (7/10) is the same as 7 units up and 10 units over. Compare this with the slope of 7 (7/1) which is 7 units up and only 1 unit over. The vertical distance is much greater than the horizontal and thus it is steeper.

A vertical line has infinitely many values of but only one value of . Thus, vertical lines are of the form , where is a real number. The only equation of this form is .

A horizontal line has infinitely many values for , but only one possible value for . Thus, it is always of the form , where is a constant. Horizontal lines have a slope of . The only equation of this form is .

The equation is a vertical line, so the perpendicular line must be horizontal. The only answer choice that is a horizontal line is .

A vertical line is only dependent on and is completely independent of . Therefore, since I is , I is a vertical line. II is not a vertical line since it is only dependent upon ; it is in fact a horizontal line.

For III, if we simplify the equation

it becomes

and finally

Since III is only dependent upon , III is a vertical line.

IV is codependent upon both and , so it is neither a vertical nor a horizontal line. Therefore, only I and III are vertical lines.

The graph of x=5 is a vertical line. The equation x=5 represents all points with x- value equal to 5.

Try to plot a couple of points with an x-value of 5.

A few examples are (5, 0), (5, 2), (5,5).

Draw a line connecting the points and you obtain a vertical line intercepting the x-axis at (5,0).

Think about the meaning of a vertical line on the coordinate grid. The value changes to any value, yet the value always stays the same. Thus, we are talking about an equation in which the is free, or is not effected, and the is constant. This is an equation of the form , where is a constant.

Think about what it means to be a horizontal line. The value changes to be any real number, but the value always remains constant. Thus, we are looking for an equation in which the value is constant and the value is not present. This would be any equation of the form , where is a constant.

The equation for a vertical line is where is the -coordinate of the point on the line.

As such, the equation for the line containing the point is,

.

The equation for a horizontal line is

where b is the y-coordinate of the point on the line.

As such, the equation for the line containing the point (7, 10) is

The slope of a line is defined as the change in the y direction divided by the change in the x direction. A vertical line does not change in the y direction nor the x direction. This means that it's slope is . It is impossible to divide any number by zero, therefore the answer is undefined.

Which of the following represents a horizontal line?

A horizontal line can be thought of as one which has the same y value for every possible value of x. In other words, it is a straight line which does not rise or fall and just remains flat at the same y-value for ever in all directions.

Rule out any choices with a variable (x for instance), and you are left with only two options.

Choose option: , because regardless of the location in x, y will always be the same.

Option: is a vertical line, because for all values of y, x will always be the same.

A vertical line on the graph must have all the points connected such that only the y-values can change, but not the x value. The value of must remain constant.

If the equation starts with a variable, and the equation is in slope intercept form, , the equation of the function would either be slanted with a positive or negative slope or horizontal, but cannot be vertical.

The equations and are not linear.

The only valid answer is:

By definition this is a vertical line and all vertical lines have a slope that is undefined.

Write the slope intercept form.

For a line to be horizontal, the value of , or slope, must be zero. The value of , or the y-intercept can be any constant number.

If the line is described by , and has no variable, the line will be vertical.

The only answer that will be horizontal is:

Horizontal lines are written as the funciton y= a number.

The two lines that demonstrate this are II. and V.

By definition, a vertical line is written as x=a number.

None of these equations are written in this format so your answer is None of the above.

Step 1: We need to determine the difference between horizontal and vertical lines.

Horizontal lines have an equation, .
Vertical Lines have an equation, .

Step 2: We want the answer that is not a horizontal line. There are three equations with and with . The is the odd one out.

The line that is not horizontal is

Any equation given that has a y-variable in the equation is incorrect. For a line to be vertical, the constant of the x-value cannot change.

This indicates that in order to be a vertical line.

The answer is: