Question

Please help me!!
The graph of line l is shown below

Which of the following is an equation for a line that is parallel to line l in the graph?
A) x = 5 y
B) x = −2
C) y = 5
D) y = −5 x

Answer 1

Given:

Points on the line are (5, 7) and (5, -5).

To find:

Equation of a line parallel to line l.

Solution:

Let us first find the slope of line l.

Slope of the line formula:

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

$m=\frac{-5-7}{5-5}$

$m=\frac{-12}{0}$

m = undefined

The line intersects at x-axis, so the y-intercept is 0.

Equation of line l is x = 5.

If two lines are parallel, then their slopes are equal.

In the option, find the line which also have slope undefined.

Option A: x = 5y

Divide by 5 on both sides, we get

$\frac{x}{5} =y$

Here slope is $\frac{1}{5}$. So it is not parallel to line l.

Option B: x = -2

Here, the slope is undefined. It also passes through the x-axis.

Therefore, it is parallel to line l.

Option C: y = 5

Here, the line passes through y-axis.

So, it is not parallel to line l.

Option D: y = -5x.

Here, the slope is -5.

So, it is not parallel to line l.

Hence x = -2 is and equation for a line that is parallel to line l in the graph.