Line (1, 1) (1, 4) Step by Step

Step by step

Question: find the equation of the line through (1, 1) and (1, 4).

(1, 1) and (1, 4)

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

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 (1, 4).

The first point is (1, 1).

m = 4 − 11 − 1

4 minus 1 is 3.

1 minus 1 is 0.

m = 30

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 = 1.

So the line is x = 1.

x = 1

Answer

m = undefined