Options:
A. [tex]y-1 = 4(x + 8)[/tex]
B. [tex]y = -4x + 15[/tex]
C. [tex]16x + 4y = 9[/tex]
D. [tex]y=-4x[/tex]
E. [tex]4x + 2y = 3[/tex]
Answer:
B. [tex]y = -4x + 15[/tex]
C. [tex]16x + 4y = 9[/tex]
D. [tex]y=-4x[/tex]
Step-by-step explanation:
Given
[tex]8x + 2y = 7[/tex]
Required
Select all equations that could be used.
Equation that could be used in place of [tex]8x + 2y = 7[/tex] must have the same slope.
Calculating the slope of [tex]8x + 2y = 7[/tex]
Make y the subject
[tex]2y = 7 - 8x[/tex]
[tex]y = \frac{7}{2} - \frac{8x}{2}[/tex]
[tex]y = \frac{7}{2} - 4x[/tex]
[tex]y = - 4x + \frac{7}{2}[/tex]
Using y = mx + b
Where
[tex]m = slope[/tex]
The slope is -4
Option A.
[tex]y-1 = 4(x + 8)[/tex]
Open bracket
[tex]y - 1=4x + 32[/tex]
Collect Like Terms
[tex]y - 4x = 32 + 1[/tex]
[tex]y - 4x = 33[/tex]
Make y the subject
[tex]y = 4x + 33[/tex]
The slope of this line is 4;
Hence, it can not be used.
Option B.
[tex]y = -4x + 15[/tex]
The slope of this line is -4;
Hence, it can be used.
Option C.
[tex]16x + 4y = 9[/tex]
Solve for4y
[tex]4y=9 - 16x[/tex]
Solve for y
[tex]\frac{4y}{4} =\frac{9}{4} - \frac{16x}{4}[/tex]
[tex]y =\frac{9}{4} - 4x[/tex]
[tex]y = - 4x + \frac{9}{4}[/tex]
The slope of this line is -4;
Hence, it can be used.
D. [tex]y=-4x[/tex]
The slope of this line is -4;
Hence, it can be used.
E. [tex]4x + 2y = 3[/tex]
Solve for 2y
[tex]2y = 3 - 4x[/tex]
Solve for y
[tex]\frac{2y}{2} = \frac{3}{2} - \frac{4x}{2}[/tex]
[tex]y = \frac{3}{2} - 2x[/tex]
The slope of this line is -2;
Hence, it can not be used.
From the calculations above, equations B, C and D are equivalent
