Question

Write the equation of the line that passes through (4,-1) that is parallel to the line 2y+6x=14

Answer 1

2y+6x= 14 is the same as y= -3x+7

To find the parallel equation you need a slope that is the same as the equation you stated first. So the slope here is -3.
Now you need this slope to go through the lines (4,-1). To do this you need to plug in these coordinates into the equation y-ysub1=slope (x-xsub1).

After plugging in it should look something like this y--1=-3(x-4).
And you can solve it from there to find the answer.