Question

Which choice is the equation of a line that passes through (9, -3) and is parallel to the line represented by this equation? y=5/3x-4

Answer 1

`y+3=(5)/(3)(x-9)` or
`y=(5)/(3)x-18`

Explanation:

step 1

Find the slope of the line parallel to the given line

we know that

If two lines are parallel, then their slopes are the same

we have

`y=(5)/(3)x-4`

therefore

The slope m of the line parallel to the given line is

`m=(5)/(3)`

step 2

Find the equation of the line in point slope form

`y-y1=m(x-x1)`

we have

`m=(5)/(3)`

`point\ (9,-3)`

substitute

`y+3=(5)/(3)(x-9)` ----> equation of the line in point slope form

step 3

Find the equation of the line in slope intercept form

`y=mx+b`

we have

`y+3=(5)/(3)(x-9)`

Isolate the variable y

`y+3=(5)/(3)x-15`

`y=(5)/(3)x-15-3`

`y=(5)/(3)x-18`