Question

What is the equation of the line (in slope-intercept form) that is parallel to y=6x−1 and passes through the point (−3,4)?

Answer 1

`y=6x+22`

Explanation:

We do not have enough information for slope intercept form. But we can use the point-slope formula to find the information. The formula is
`y -y_(1) =m(x -x_(1))` where we substitute a point (x,y) for
`(x_(1),y_(1))`.

We know it is parrallel to the listed line in slope intercept form. Recall, y=mx+b tells that the m is slope. Since y=6x-1, then m=6. We also have a point for the new line (-3, 4). We input m and
`x_(1) =-3\\y_(1)=4`.

`y-4=6 (x-(-3))\\y-4=6 (x+3)`

We now simplify the parenthesis and solve for y.

`y-4=6x+6(3)\\y-4=6x+18`

We add 4 to both sides to isolate y,

`y-4+4=6x+18+4\\y=6x+22`

This is slope intercept form. The line as slope 6 and y-intercept (0,22) or b=22.