Question

Find the slope of the line passing through the points (8,-3) and (4,-7)

Answer 1

The slope, commonly abbreviated as
`m`, is the change in the quantity on the y-axis, Δy, divided by the change in the quantity on the x-axis, Δx.

`m = (\Delta y)/(\Delta x) = (y2 - y1)/(x2 - x1)`

From the points (x, y), the first value is a value on the x-axis, and the second value after the comma is a value on the y-axis. So for the point (8, -3), 8 is x and -3 is y. But we have two points, so:

(8, -3), 8 is x1, -3 is y1

(4, -7), 4 is x2, -7 is y2

Plugging in our values, we get

`m = (y2-y1)/(x2-x1) = (-7-(-3))/(4-8) = (-7 + 3)/(-4) = (-4)/(-4) = 1`

So the slope,
`m`, is equal to 1.