Question

Choose all the lines that are parallel to the line pictured in the graph bellow.

Answer 1

Answer:

a. y = -½x

b. y = -½x + 3

c. 2y = -x - 4

e. x + 2y = 8

Step-by-step explanation:

Parallel lines have the same slope. Therefore, the lines that will be parallel to the given line on the graph would have the same slope as the line of the graph.

First, find the slope of the line on the graph:

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

Use the coordinates of any two points on the line. Let's use (-4, 0) and (0, -2)

$m = \frac{-2 - 0}{0 -(-4)} = \frac{-2}{4} = -\frac{1}{2}$

Slope of the line on the graph is -½.

Check each given line equation, ensure they are in the slope-intercept form and find out if the value of their slope is the same as -½.

Slope-intercept form is given as y = mx + b, where, m = slope.

Option 1: y = -½x

The slope of this line is -½, therefore it is parallel to the line on the graph.

Option 2: y = -½x + 3

The slope of this line is also -½, therefore it is parallel to the line on the graph.

Option 3: 2y = -x - 4

Rewrite in slope-intercept form.

y = -x/2 - 4/2

y = -½x - 2

The slope of this line is -½, therefore it is parallel to the line on the graph.

Option 4: y = 2x - 5.

The slope of this line is 2, therefore it is NOT parallel to the line on the graph.

Option 5: x + 2y = 8

Rewrite in slope-intercept form.

2y = 8 - x

y = 8/2 - x/2

y = 4 - ½x

The slope of this line is -½, therefore it is parallel to the line on the graph.