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