Question

Write an equation in slope-intercept form for the line that passes through the given points and is (a) parallel to the given line and (b) perpendicular to the given line. 1. (-7,3);x=4
2.(5,-1);y=4x-7
Please help!!

Answer 1

Remark
This is costing you an awful lot of points, but it is a little hard to read. If I'm not interpreting it correctly, leave some sort of note below my answer.

Question One
In the first question you want a line that is parallel to x = 4 and goes through the point (-7,3). If I'm reading this correctly then the line you want is x = -7. You only need the x value of the given point. I'll put a graph there to show you what it looks like on a grid.  The graph is the left one for this question.

Question Two
Here I think you want the line going through (5,-1) and perpendicular to y = 4x - 7. I will make a graph for that one as well.

Begin with the slope
Two lines are perpendicular to each other if their slopes multiply to - 1
Given slope (m1) = 4
perpendicular slope = m2

Formula
m1 * m2 = - 1
4 * m2 = -1      Divide by 4
m2 = -1/4

So far what you have is
y = (-1/4)x + b

Now use the given point to solve for b
x = 5
y = - 1
b = ??

-1 = (-1/4)*5 + b
-1 = -5/4 + b  Add 5/4 to both sides
-1 + 5/4 + b   Make -1 into -4/4
b = -4/4 + 5/4
b = (-4 + 5)/4
b = 1/4

So the line that you want is
y = (-1/4) x + 1/4

Answers
One:  x = - 7
Two: y = (-1/4)x + 1/4

Note
The right graph is of y = 4x - 7 and y = (-1/4)x + 1/4