Question

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

Answer 1

Answer:

The value of j = -5

Step-by-step explanation:

Given the points of the line

• (j, – 9)

• ( – 10, – 4)

Slope m = -1

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

$m=\frac{y_2-y_1}{x_2-x_1}$

Here:

• $\left(x_1,\:y_1\right)=\left(j,\:-9\right)$

• $\left(x_2,\:y_2\right)=\left(-10,\:-4\right )$

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

$m=\frac{-4-\left(-9\right)}{-10-j}$

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

$-1=\frac{-4-\left(-9\right)}{-10-j}$

Multiply both sides by -10 -  j

$-1\cdot \left(-10-j\right)=\frac{5}{-10-j}\left(-10-j\right)$

Simplify

$-\left(-10-j\right)=5$

Divide both sides by -1

$\frac{-\left(-10-j\right)}{-1}=\frac{5}{-1}$

Simplify

$-10-j=-5$

Add 10 to both sides

$-10-j+10=-5+10$

Simplify

$-j=5$

Divide both sides by -1

$\frac{-j}{-1}=\frac{5}{-1}$

Simplify

$j=-5$

Therefore, the value of j = -5

Verification:

As the value of j = -5

Now we have the points

• (-5, – 9)

• ( – 10, – 4)

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)

$m=\frac{y_2-y_1}{x_2-x_1}$

Here:

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

$m=\frac{-4-\left(-9\right)}{-10-\left(-5\right)}$

$m=\frac{-4+9}{-10+5}$

$m=\frac{5}{-5}$

Apply fraction rule:  $\frac{a}{-b}=-\frac{a}{b}$

$m=-\frac{5}{5}$

$m=-1$

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