The points (j, – 9) and ( – 10, – 4) fall on a line with a slope of – 1. What is the value of j?

The value of j = -5

Step-by-step explanation:

Given the points of the line

Slope m = -1

To determine the value of j, we need to use the slope formula

Here:

Now, substitute (x₁, y₁) = (j, -9)  and (x₂, y₂) = (-10, -4) in the formula

We are already given m = -1. Therefore, we need to substitute m = -1 in the formula and solve for j

Multiply both sides by -10 -  j

Simplify

Divide both sides by -1

Simplify

Add 10 to both sides

Simplify

Divide both sides by -1

Simplify

Therefore, the value of j = -5

Verification:

As the value of j = -5

Now we have the points

Now, we need to check whether the slope between the points (-5, -9) and (-10, -4) is -1 or not.

Let us determine the slope between the points (-5, -9) and (-10, -4)

Here:

Now, substitute (x₁, y₁) = (-5, -9)  and (x₂, y₂) = (-10, -4) in the formula

Apply fraction rule:  

Therefore, we verified that the slope of the line containing the points (-5, -9) and (-10, -4) is indeed m = -1.