Algebra II - Vertical and Horizontal Lines

Which of the following is a horizontal line?

Explanation

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 .

Which of the following equations will represent a horizontal line?

$y=\frac{1000}{x}$

Explanation

The slope intercept form of an equation refers to a linear line with a certain slope and y-intercept.

In order for the line to be horizontal, the slope must equal to zero.

Any equation in the answer choices that has an x-variable is incorrect because this either means that the equation has a existing slope, a vertical line, or it's non-linear.

The best answer is:

Which of the following is a vertical line?

Explanation

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 .

What is the equation for the horizontal line containing the point ?

Explanation

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

Which of the following answers is considered a vertical line?

$x=\frac{1}{4}$

$y=\frac{1}{x}$

Explanation

A vertical line has an undefined slope. This also means that the x-value is fixed for every y-value of the graph.

The slope intercept form for a linear equation is . If , the slope would indicate that the line is horizontal.

Any answer that has a in the equation is incorrect.

The only valid answer is: $x=\frac{1}{4}$

Which of these lines is the steepest or would be most difficult to walk up if the line represented a ramp?

Explanation

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.

$\boldsymbol{y=4x+5}$

Which of the following graphs exhibit a horizontal line?

$y=\textup{constant}$

$x= \textup{constant}$

$x+y=\textup{constant}$

$y=\frac{1}{x}$

Explanation

The horizontal line will always have zero slope.

In the form , the term must be zero for a horizontal line.

The forms $y=\frac{1}{x}$ and are non-linear.

A constant is a fixed number that will not change.

The equation $x= \textup{constant}$ represents a vertical line.

The only possible answer is: $y=\textup{constant}$

Which of the following answers describes the graph of this equation?

(Select all answers that apply)

vertical line

horizontal line

Not enough information

Explanation

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).

II)

III)

IV)

Which of the presented equations are vertical lines?

I and III

I and II

II and IV

III and IV

Explanation

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.