Question

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.

Answer 1

Options:

A.
`y-1 = 4(x + 8)`

B.
`y = -4x + 15`

C.
`16x + 4y = 9`

D.
`y=-4x`

E.
`4x + 2y = 3`

Answer:

B.
`y = -4x + 15`

C.
`16x + 4y = 9`

D.
`y=-4x`

Explanation:

Given

`8x + 2y = 7`

Required

Select all equations that could be used.

Equation that could be used in place of
`8x + 2y = 7` must have the same slope.

Calculating the slope of
`8x + 2y = 7`

Make y the subject

`2y = 7 - 8x`

`y = (7)/(2) - (8x)/(2)`

`y = (7)/(2) - 4x`

`y = - 4x + (7)/(2)`

Using y = mx + b

Where

`m = slope`

The slope is -4

Option A.

`y-1 = 4(x + 8)`

Open bracket

`y - 1=4x + 32`

Collect Like Terms

`y - 4x = 32 + 1`

`y - 4x = 33`

Make y the subject

`y = 4x + 33`

The slope of this line is 4;

Hence, it can not be used.

Option B.

`y = -4x + 15`

The slope of this line is -4;

Hence, it can be used.

Option C.

`16x + 4y = 9`

Solve for4y

`4y=9 - 16x`

Solve for y

`(4y)/(4) =(9)/(4) - (16x)/(4)`

`y =(9)/(4) - 4x`

`y = - 4x + (9)/(4)`

The slope of this line is -4;

Hence, it can be used.

D.
`y=-4x`

The slope of this line is -4;

Hence, it can be used.

E.
`4x + 2y = 3`

Solve for 2y

`2y = 3 - 4x`

Solve for y

`(2y)/(2) = (3)/(2) - (4x)/(2)`

`y = (3)/(2) - 2x`

The slope of this line is -2;

Hence, it can not be used.

From the calculations above, equations B, C and D are equivalent