Question

(-4, 7), (-6,-4) find the slope of the line through each pair of points

Answer 1

Answer:

slope = 11/2

Step-by-step 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

Answer 2

$\huge\boxed{\frac{11}{2}}$

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:

$\dfrac{y_2-y_1}{x_2-x_1}$

Substitute the values and simplify to find the answer.

$\dfrac{(-4)-7}{(-6)-(-4)}$

$\dfrac{-4-7}{-6+4}$

$\dfrac{-11}{-2}$

$\boxed{\frac{11}{2}}$