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=(y_2-y_1)/(x_2-x_1)`

Checking A:

`m=(-4-2)/(1-3)=-(6)/(-2)=3`

Not correct.

Checking B:

`m=(2-2)/(3-1)=0`

Not correct.

Checking C:

`m=(0-2)/(0-3)=(2)/(3)`

Not correct.

Checking D:

`m=(0--2)/(-2--1)=(2)/(-1)=-2`

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

Correct Answer is D