Step by step
The question
Question: find the equation of the line through (−2, 3) and (−2, −1).
(−2, 3) and (−2, −1)
Every line that is not straight up and down is y = mx + b.
m is the slope.
b is where the line crosses the y-axis: where we start.
So we need m and b.
y = mx + b
m = slope
b = start
1 Find the slope
We call the slope m.
m = rise over run.
m = riserun
The top is the change in y: second y minus first y.
The bottom is the change in x: second x minus first x.
m = y2 − y1x2 − x1
Put the numbers in.
The second point is (−2, 3).
The first point is (−2, −1).
m = 3 − (−1)−2 − (−2)
Taking away a negative is the same as adding.
− (−) = +
So it becomes (3 + 1) over (−2 + 2).
m = 3 + 1−2 + 2
3 plus 1 is 4.
−2 plus 2 is 0.
m = 40
The bottom is 0.
We cannot divide by 0.
So there is no number for the slope.
We say the slope is undefined.
m = undefined
A straight up and down line is not y = mx + b.
Every point on it has x = −2.
So the line is x = −2.
x = −2
Answer
m = undefined