Fred's art project involves a series of parallel stripes If he starts by drawing the line 8x + 2y = 7, select all the equations that could represent lines

that could also be drawn for his art project

A. y-1 = 4 (X + 8)

B. y = - 4x + 15

C. 16x + 4y = 9

D. y=-4X

E. 4x + 2y = 3

B. y = - 4x + 15

C. 16x + 4y = 9

D. y=-4X

Step-by-step explanation:

Two lines are parallel if they have the same slope. The equation of a line is:

y = mx + b

Where m is the slope and b is a constant.

So, the slope of the first equation can be calculated solving the equation for y as:

8x + 2y = 7

2y = - 8x + 7

y = - 4x + 7/2

So, the slope is - 4.

It means that all the equations that could represent lines that could also be drawn for his art project are the equation with a slope equal to - 4.

Then, for every option, we get:

A. y-1 = 4 (X + 8)

y = 4x + 32 + 1

The slope is 4

B. y = - 4x + 15

The slope is - 4

C. 16x + 4y = 9

4y = - 16x + 9

y = - 4x + 9/4

The slope is - 4

D. y=-4X

The slope is - 4

E. 4x + 2y = 3

2y = - 4x + 3

y = - 2x + 3/2

The slope is - 2

Finally, the equations that are parallel to the line 8x + 2y = 7 are equations B, C and D