Question

1. Using the line y=2x - 7 as a reference, describe how to determine the equation of a line that is perpendicular and another line that is parallel to this given line.
2. What is the relationship between the two lines below?
A. Parallel
B. Perpendicular
C. The two lines intersect in exactly one point.
D. The two lines intersect in infinitely many points.
3. What is the equation of the line that is parallel to the line drawn through the points C and D? Please show the steps to your solution?
C=2, 1 and D=0, 0

Answer 1

and also: 4. What is a possible equation of a line that is perpendicular to the line drawn through points A and E? Please show the steps to your solution.
A = -6, 3 and E = -4, -5.

Answer 2

1. You would look at the slope and if it's the same then it's parallel. If it's opposite reciprocal, then it would be perpendicular.
2. I don't see the the 2 lines...
3. To figure out this problem, you must know the slope-intercept formula.
y=mx+b
m=slope
b=y-intercept (0,y)

Point D is (0,0) so slope intercept is 0
y=mx+0

Point C is (2,1), which is a solution to the line. We can put that in our equation

1=m(2)+0
Divide each side by 2
1/2=m

We now know all the necessary variables.
y=(1/2)x+0
We can leave that 0 out because it has no effect on the equation
y=(1/2)x

4. This time you would have 2 equations but you would plug in those variables for x and y. You can solve for it using substitution, elimination or matrices. Elimination is generally quicker and easier.
Here's to get you started

For point A(-6,2)
2=m(-6)+b

For point E
-5=m(-4)+b