How do I do this maths work?

Question

there are a total of 45 slope questions for homework, 15 of each of the follwoing kind. School was dismissed early due to weather, and the Math teacher was unable to get to how we do this...but she still expects us to get it done. We have learned the slope formula, but i am not sure how to put in each numbers in the correct position:

question #1-
Find the value of K so that the line joining the points (-2, 7) and (3, K) is horizontal

Graphically, i found K=7, but we have to show it in algebraic form.

question #16-
Find the value of K so that the line joining points (1, -3) and (k, 5) is vertical.

Same situation as above, i found K=1 but have no clue how to do it algebraically.

question #31-
If the line joining points P(3,5) and Q(1,2) is paralell to line joining
R(7,K) and S(5,6), What is the value of K?

This one, i have no idea how to do at all!

any help greatly appreciated!!!

Answer 1

You can add this to the answer, horizontal y - y = 0, vertical x - x = 0
7 - K = 0
K = 7
1 - i = 0
i = 1
For the parallel line:
P(x) - Q(x) = 2
3 - 1 = 2
P(y) - Q(y) = 3
5 - 2 = 3
so
5 - 7 = 2
k - 6 = 3
k=9
This is to help explain the result.

Answer 2

The slope of all horizontal lines is zero.
The slope of all vertical lines is infinity.

For the last one, the two lines have the same slope, but different y-intercepts.

Use the m= formula and the two known points to get the slope of both lines.
.
Then use y = mx + b and the known point on the other line to find the y-intercept (x=0)

Proof:

y2 - y1
m = ---------
x2 - x1


7 - 7 0
m= ------------- = -----
3 - (-2) 5

Another way:

y=mx+b basic formula of a line

7 = -2m + b must be true
7 = 3m + b must also be true.

multiply top equasion by 2 & bottom by 2

21 = -6m + 3b
14 = 6m + 2b

add both equasions

35 = 5b
7 = b

plug into either equasion & solve for m

7 = 3m + 7
0 = 3m
0 = m

Answer 3

for the 1st one, remember y2-y1 x2-x1, where (-2 is x1, 7 is y1) and (3 is X2, 7 is Y2) use the y2-y1, x2-x1 and thats your slope

Answer 4

just use acalulator are go to the learning center