Question

(Attachment)

100 POINTS!!
Which line is parallel to the line shown below?

I know D is right but I’m not sure how to get the answer.. it’s been way too long.

Answer 1

Answer: Your answer will be D.
`4x-3y=15`

Answer 2

D. 4x - 3y = 15

Explanation:

The slope of a line is defined as the "change in y" over the "change in x".

This is also commonly referred to as "rise over run".

From inspection of the graphed line, we can see that the "rise" between the two points is 4 units up, and the "run" between to the two points is 3 units right. "Up" and "right" are positive directions, therefore the slope of the line is ⁴/₃.

The given answer options are all in standard form.

The standard form of a linear equation is Ax + By = C, where A, B and C are constants and A is positive.

The slope of a linear equation in standard form is -A/B.

If two lines are parallel, they have the same slope.

Therefore:

`\implies \sf (4)/(3)=-(A)/(B)`

Remember that the constant A is positive, so this means that A=4 and B=-3. Therefore, we are looking for an answer option that includes "4x - 3y" on the left side of the equation.

Therefore, the line that is parallel to the graphed line is:

• 4x - 3y = 15