Q33. - Algebra 2

Question

33. What is the slope of a line parallel to $y-2=4\left(x+1\right)$?

$\text{A}.\text{ -4 B. }\frac{-1}{4}\text{ C.}\frac{1}{4}\text{ D.4}$

Step-by-Step Solution

Answer

The slope of a line parallel to $y-2=4\left(x+1\right)$ is 4.

Step-1 – Apply the concept of slope-intercept form

The slope of a line is the ratio of the change in the y-coordinates to the change in the x- coordinates.

The slope-intercept form of the equation of a line is given by $y=mx+b$ where m is the slope and b is the y-intercept.

Step-2 – Simplify the equation

Given line is $y-2=4\left(x+1\right)$. Simplifying the given line the following is obtained

$\begin{array}{c}y-2=4\left(x+1\right)\\ \Rightarrow y-2=4x+4\\ \end{array}$

Step-3 – Convert the equation of the given line into slope-intercept form

In order to convert the equation obtained in step 2 into the slope intercept form, keep the variable y on the left-hand side and bring rest of the things to the right-hand side. Therefore,

$\begin{array}{c}\Rightarrow y-2+2=4x+4-2\text{ (add 2 on both sides)}\\ \Rightarrow y=4x+2\end{array}$

This is of the form $y=mx+b$

Hence, the slope is m = 4

Therefore, option D is correct.