Geometry, equations of parallel and perpendicular lines

Question

How do you solve this?

Directions:
Write an equation of the line that passes through the given point and is parallel to the given line.

Questions:
1. (1,7), -6x + y = -1
2. (-2,5), 2y = 4x - 6

I would really appreciate it if someone helped me by doing a step-by-step process, I was really tired and unfortunately wasn't paying attention in class when we were learning this, thank you.

Answer 1

I will work the first one for you, and you try the second one.

 

-6x + y = -1 

 

It is convenient to express this in the form

 

y = mx + b

 

y = 6x - 1

 

If parallel, it must have the same slope.

 

m = 6

 

So far, we have 

 

y = 6x + b

 

Use the given point to find b.

 

7 = 6(1) + b

b = 7 - 6 = 1

 

y = 6x + 1