SAT Parallel and Perpendicular Lines

Correct Answer: C

Solution :

Tip: Slope-intercept form: $y=mx+b,$ where $m$ is the line's slope, and $b$ its $y$ -intercept.
Re-written in slope-intercept form the given equation becomes:

$\begin{array}{rcl} 2x &=& 4y + 8\\ 4y + 8 &=& 2x\\ 4y &=& 2x-8\\ y &=& \frac{1}{2}x - 2\\ \end{array}$

The slope of this line is $m = \frac{1}{2}$ .

We check this against the slope of each of the options.

(A) In slope-intercept form $2x + 4y + 8 = 0$ becomes

$\begin{array}{rcl} 2x + 4y + 8 &=& 0\\ 4y +8 &=&-2x\\ 4y &=&-2x-8\\ y &=&-\frac{1}{2}x-2\\ \end{array}$

The line has slope $- \frac{1}{2} \neq \frac{1}{2}$ . Wrong choice.

(B) In slope-intercept form $4x = 2y + 8$ becomes

$\begin{array}{rcl} 4x &=& 2y + 8 \\ 2y+8 &=&4x\\ 2y &=&4x-8\\ y &=&2x-4\\ \end{array}$

This line has slope $2 \neq \frac{1}{2}$ . Wrong choice.

(C) In slope-intercept form $8y = 4x + 2$ becomes

$\begin{array}{rcl} 8y &=&4x + 2 \\ y &=&\frac{1}{2}x+\frac{1}{4}\\ \end{array}$

This line has slope $\frac{1}{2} = \frac{1}{2}$ . This is the answer.

(D) In slope-intercept form $4x + 8y = 2$ becomes

$\begin{array}{rcl} 4x + 8y &=& 2 \\ 8y &=& -4x+2\\ 8y &=& -4x +2\\ y &=& -\frac{1}{2}x +\frac{1}{4}\\ \end{array}$

This line's slope equals $-\frac{ 1}{2} \neq \frac{1}{2}$ . Wrong choice.

(E) In slope intercept form $2x - 8y = 4$ becomes

$\begin{array}{rcl} 2x - 8y &=& 4\\ -8y &=& -2x+4\\ y &=& \frac{1}{4}x + \frac{1}{2}\\ \end{array}$

This line's slope equals $\frac{1}{4} \neq \frac{1}{2}$ . Wrong choice.

Hence the answer is (C).

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Incorrect Choices:

(A) , (B) , (D) and (E)
Look at the Solution for how to eliminate these choices.