Question

Which lines are parallel to the graph of 4x – y = 6? Check all that apply.

Answer 1

Hello :
4x – y = 6
y = 4x+6 the slope is : 4

 lines are parallel to the graph of 4x – y = 6 is : y = 4x + 11 and :y + 1 = 4(x – 2)
(same slope)

Answer 2

Answer:

The lines which are parallel to the graph of $4x-y=6$ are:

3)    $y+1=4(x-2)$

4)    $y=4x+11$

6)      $8x-2y=6$

Step-by-step explanation:

We are given a equation of line as:

$4x-y=6$

on changing this line to the slope-interceot form of a line:

$y= mx+c$ where m denotes the slope of the line and c denotes the y-intercept we get:

$y=4x-6$

i.e. the slope of line is 4.

Also we know that the slope of parallel line is equal.

so we will check in each of the following options whose slope is 4.

1)

$x-4y=-12$

This equation could also be represented as:

$4y=x+12\\\\y=\dfrac{1}{4}x+\dfrac{12}{4}\\\\y=\dfrac{1}{4}x+3$

Hence its slope is $\dfrac{1}{4}$ which is not equal to 4.

Hence option 1 is incorrect.

2)

$y-2=-4(x+1)\\\\y=2-4(x+1)\\\\y=2-4x-4\\\\y=-4x-2$

Hence, it's slope is -4 which is not equal to 4.

Hence, option 2) is incorrect.

3)

$y+1=4(x-2)$

This equation could also be represented as:

$y=-1+4(x-2)\\\\y=-1+4x-8\\\\y=4x-9$

Hence, the slope of line is 4.

Hence, option 3 is correct.

4)

$y=4x+11$

Clearly the slope is 4.

Hence, the line is parallel.

Hence, option 4 is true.

5)

$y=x-3$

Clearly the slope is 1.

Hence, the line is not parallel to the given line.

Hence, option 5 is incorrect.

6)

$8x-2y=6$

This equation could also be represented as:

$8x-6=2y\\\\y=4x-3$

Clearly the slope is 4.

Hence, the line is parallel.

Hence, option 6 is true.