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. $y=-4x$

Step-by-step 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

$2y = 7 - 8x$

$y = \frac{7}{2} - \frac{8x}{2}$

$y = \frac{7}{2} - 4x$

$y = - 4x + \frac{7}{2}$

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

$\frac{4y}{4} =\frac{9}{4} - \frac{16x}{4}$

$y =\frac{9}{4} - 4x$

$y = - 4x + \frac{9}{4}$

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

$\frac{2y}{2} = \frac{3}{2} - \frac{4x}{2}$

$y = \frac{3}{2} - 2x$

The slope of this line is -2;

Hence, it can not be used.

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