Question

What is the slope of the line containing
the ordered pair (2, 3) and (-4,0)?

Answer 1

slope =
`(1)/(2)`

Explanation:

Calculate slope m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (2, 3) and (x₂, y₂ ) = (- 4, 0)

m =
`(0-3)/(-4-2)` =
`(-3)/(-6)` =
`(1)/(2)`

Answer 2

The slope of the line passing between these points is 1/2

Explanation:

slope is equal to the difference vertically divided by the difference horizontally, moving left to right.

In this case, (2, 3) is further left, so we'll subtract (-4, 0) from that.

(2, 3) - (-4, 0) = (6, 3)

So we know the displacement is (6, 3) and we need simply delete dy by dx:

s = Δy/Δx

s = 3/6

s = 1/2

So we have a slope of one half, describing a line that moves up, left at a 45 degree angle from the horizontal.