Question

What is the equation of the line that is parallel to the given

Answer 1

Answer

O 4x+3y=-6

Step-by-step explanation:

Hello, I can help you witht this,

to solve this you need

step one

the line we are looking for is paraller to the line in the graph, it means both of then have the same slope.

find the slope of the line in the graph

remember

to find the slope of a line with two known points you can use

Let

$P1(x_{1},y_{1})}\\P1(x_{2},y_{2})\\slope\\s=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

pick two points from he graph

P1(0,3)

P2(3,-1)

put the values into the equation

$slope(m)\\m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\m=\frac{-1-3}{3-0}\\m= \frac{-4}{3}$

so, the slope of the line we are looking for is m=-4/3  and passes through the point (-3,2)

step 2

use the equation

$y-y_{1}=m(x-x_{1})$

to ding the equation of the line

P1(-3,2)

$y-y_{1}=m(x-x_{1})\\y-2=\frac{-4}{3} (x+3})\\isolate\ y\\y-2=\frac{-4x}{3}-4\\y=\frac{-4x}{3}-4+2\\y+\frac{4x}{3}=-2\\multiply\ each\ side\ by\ 3\\3(y+\frac{4x}{3})=3*-2\\\\3y+4x=-6\\4x+3y=-6$

and that's all, that is the equation of the line that is parallel to the given

line and passes through the point (-3, 2).

Have a good day.