Question

QUESTION 52What is the equation of a line that is parallel to y=x+6 and that passes through the point (3,-1)?3OA.2Ay-x-3O B.2y=x+33OC. y=-3²2O D.y =I-x-1-332H

Answer 1

Given:

There is a equation of line given as:

$y=\frac{2}{3}x+6$

Required:

We need to find the parallel line to the given line which is passes through (3,-1)

Explanation:

Here compare given equation with

$y=mx+b$

so the m=2/3 which is the slope of given line

We need to find the parallel line to the given line it means the slope of both lines is same

so the slope of required line is also m=2/3

now to find the required line which is passes through (3,-1)

there is a formula

$y-y_1=m(x-x_1)$

where

$(x_1,y_1)=(3,-1)$

now substitute the all values in the formula

$\begin{gathered} y-(-1)=\frac{2}{3}(x-3) \\ \\ y+1=\frac{2}{3}(x-3) \\ \\ y=\frac{2}{3}x-1-2 \\ \\ y=\frac{2}{3}x-3 \end{gathered}$

Final answer:

Parallel line to the given line is

$y=\frac{2}{3}x-3$