Question

6. Which of the following points would lie on a line that is parallel to y = -2x + 3 (A) (3,2) and (1, -4) (B) (1,2) and (3,2) (C) (3,-2) and (0,0) (D) (-1,-2) and (-2,0)

Answer 1

Parallel lines have equal slopes.

The line is in the form:

$y=mx+b$

Where m is the slope and b is the y intercept.

So, the line has slope of -2

The parallel line will have an equation:

$y=-2x+b$

Two points are given in each choice. We just need to find the slope of each answer choice with slope formula and whichever is equal to "-2" is our answer.

The slope formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

Checking A:

$m=\frac{-4-2}{1-3}=-\frac{6}{-2}=3$

Not correct.

Checking B:

$m=\frac{2-2}{3-1}=0$

Not correct.

Checking C:

$m=\frac{0-2}{0-3}=\frac{2}{3}$

Not correct.

Checking D:

$m=\frac{0--2}{-2--1}=\frac{2}{-1}=-2$

Yes, this is -2. This is the line parallel to the line given.

Correct Answer is D