Find an equation for the line parallel

Question

Find an equation for the line parallel to y=10x+2 and goes through the point (-8,6).
Write your answer in the form y=mx+b.

y=

Answer 1

When you are looking for a line that is parallel, you are going to be looking at the slope of the line. In y=mx+b format, the m represents the slope. In the equation y=10x+2, the slope (m) is 10. When dealing with parallel lines, the slope is the same. (This is because the lines will never intersect).  

Since we know that the new line will have the same slope, we will write the following new information down.

m = 10    (the parallel slope)

x = -8     (we get the x and the y from the information given to us in the form of the point (-8,6)

y = 6

We then take this new information and plug it into the equation y = mx+b in order to solve for b (the y intercept).

y=mx+b

6=10(-8) + b

6 = -80 + b

86 = b

Since we now found the b, we can take our parallel slope (10) and our y intercept (86) and plug the information back into our equation.

y = 10x + 86