Question

(-4, 7), (-6,-4)

find the slope of the line through each pair of points

Answer 1

`\huge\boxed{(11)/(2)}`

The slope is equivalent to vertical change divided by horizontal change, otherwise known as "rise over run".

Therefore, the slope can be represented with the following equation, where
`(x_1,y_1)` and
`(x_2,y_2)` are your points:

`(y_2-y_1)/(x_2-x_1)`

Substitute the values and simplify to find the answer.

`((-4)-7)/((-6)-(-4))`

`(-4-7)/(-6+4)`

`(-11)/(-2)`

`\boxed{(11)/(2)}`

Answer 2

slope = 11/2

Explanation:

If you are given two points, you can find the slope using the point-slope equation. The equation looks like this:

y₁ - y₂ = m(x₁ - x₂)

In this form, "m" represents the slope, "x₁" and "y₁" represent the values from one point, and "x₂" and "y₂" represent the values from the other point. You can plug the values from the points into the equation and simplify to find the slope.

Point 1: (-4, 7) Point 2: (-6, -4)

x₁ = -4 x₂ = -6

y₁ = 7 y₂ = -4

y₁ - y₂ = m(x₁ - x₂) <----- Point-slope form

7 - (-4) = m(-4 - (-6)) <----- Insert values

11 = m(2) <----- Simplify

11/2 = m <----- Divide both sides by 2