Question

Write an equation passing through the point and parallel to the given line. (4,7);y=3x+4

Answer 1

`y=3x-5`

Explanation:

step 1

Find the slope

we know that

If two lines are parallel, then their slopes are equal

The slope of the given line is
`m=3`

so

The slope of the line parallel to the given line is also
`m=3`

step 2

Find the equation of the line in point slope form

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

we have

`m=3`

`point\ (4,7)`

substitute

`y-7=3(x-4)`

step 3

Convert to slope intercept form

isolate the variable y

`y-7=3x-12\\y=3x-12+7\\y=3x-5`