Question

What is the equation of the line that passes through the point (4,5) and is parallel to the line whose equation is y=2/3x-4

Answer 1

`y=(2)/(3)x+(7)/(3)`

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 equal

we have

`y=(2)/(3)x-4` ---> given line

The slope of the given line is
`m=(2)/(3)`

so

the slope of the line parallel to the given line is
`m=(2)/(3)`

step 2

Find the equation of the line in point slope form

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

we have

`m=(2)/(3)`

`point\ (4,5)`

substitute

`y-5=(2)/(3)(x-4)`

step 3

Convert to slope intercept form

`y=mx+b`

isolate the variable y

`y-5=(2)/(3)x-(8)/(3)`

`y=(2)/(3)x-(8)/(3)+5`

`y=(2)/(3)x+(7)/(3)`