Question

Which lines are parallel to 8x + 2y = 7? Select all that apply. A. y − 1 = 4(x + 8) B. y = −4x + 15 C. 16x + 4y = 9 D. y = −4x

Answer 1

Answer: B. y = −4x + 15

C. 16x + 4y = 9

D. y = −4x

Step-by-step explanation:

The given equation of a line = $8x+2y=7$

Subtract 8x from both sides , we get

$2y=-8x+7$

Divide both sides by 2 , we get

$y=-4+\dfrac{7}{2}$   → which is slope-intercept form.

[An Slope -intercept form of equation of a line is y=mx+c , where m(coefficient of x)= slope of line]

⇒ The slope of the given line = coefficient of x= -4

Also, we know that if two lines are parallel then their slopes are equal.

Lets check all the options ,

A. y − 1 = 4(x + 8)

$\Rightarrow\ y=4(x+8)-1\\\\y=4x+32-1\\y=4x+31$

Slope = 4 ≠ -4

⇒ It is not parallel to the given line.

B. y = −4x + 15

Slope = -4 = slope of given line.

⇒ It is parallel to the given line.

C. 16x + 4y = 9

$\Rightarrow\ 4y=-16x+9\\\\\Rightarrow\ y=-4x+\dfrac{9}{4}$

Slope = -4 = slope of given line.

⇒ It is parallel to the given line.

D. y = −4x

Slope = -4 = slope of given line.

⇒ It is parallel to the given line.

Hence, the lines are parallel to 8x + 2y = 7 are :

B. y = −4x + 15

C. 16x + 4y = 9

D. y = −4x

Answer 2

8x + 2y = 7

2y = -8x + 7

y = -4x + 7/2; this line has slope equal -4

Parallel lines, slope is the same so slope of parallel line is also -4

A. y − 1 = 4(x + 8); slope m = 4....FALSE

B.    y = −4x + 15;  slope m = - 4....TRUE

C. 16x + 4y = 9;  4y  = -16x + 9 so y = -4x + 9/4; slope m = - 4....TRUE

D. y = −4x; slope m = - 4....TRUE

Answer

B.    y = −4x + 15

C. 16x + 4y = 9

D. y = −4x