Find the slope given the following two points: ( 16, 3) and (14, -19)

Answer 1

Slope or gradient (often referred to as m) of a line is defined as change in y coordinate / change in x coordinate.

You might have heard this referred to as "delta" y / "delta" x.

And it's handy to remember that positive gradients go up and to the right, while negative gradients go down and to the right.

The equation becomes m = (y2 - y1) / (x2 - x1) often referred to as "rise over run".

In this case, m = (-19 - 3) / (14 - 16) = -22 / -2 = 11

If you don't like this formula, you can start at the first point and then see how far you rise up (positive) or down (negative) you go to reach the second point. Then repeat horizontally, to see how far you run right (positive) or left (negative) to reach the second point.

e.g. start at (16, 3)

from y = 3 how far up or down to reach y = -19? It's 22 units. And because it's down, it's -22.

from x = 16, how far across to reach x = 14? We have to go left 2 units. And left is negative, so it's -2.

-22/-2 = 11

If you start at (14, -19) instead, it's OK too

from y = -19 how far up or down to reach y = 3? It's still 22 units. But it's up, so it's +22.

from x = 14, how far across to reach x = 16? Again 2 units. But right, so +2.

22/2 = 11

Answer 2

Slope is calculated as change in y over change in x

Y₂ - Y₁ = ΔY 3 - (-19)

X₂ - X₁ = ΔX 16 - 14