Answer:
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
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Here:
Now, substitute (x₁, y₁) = (j, -9) and (x₂, y₂) = (-10, -4) in the formula
[tex]m=\frac{-4-\left(-9\right)}{-10-j}[/tex]
We are already given m = -1. Therefore, we need to substitute m = -1 in the formula and solve for j
[tex]-1=\frac{-4-\left(-9\right)}{-10-j}[/tex]
Multiply both sides by -10 - j
[tex]-1\cdot \left(-10-j\right)=\frac{5}{-10-j}\left(-10-j\right)[/tex]
Simplify
[tex]-\left(-10-j\right)=5[/tex]
Divide both sides by -1
[tex]\frac{-\left(-10-j\right)}{-1}=\frac{5}{-1}[/tex]
Simplify
[tex]-10-j=-5[/tex]
Add 10 to both sides
[tex]-10-j+10=-5+10[/tex]
Simplify
[tex]-j=5[/tex]
Divide both sides by -1
[tex]\frac{-j}{-1}=\frac{5}{-1}[/tex]
Simplify
[tex]j=-5[/tex]
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)
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Here:
Now, substitute (x₁, y₁) = (-5, -9) and (x₂, y₂) = (-10, -4) in the formula
[tex]m=\frac{-4-\left(-9\right)}{-10-\left(-5\right)}[/tex]
[tex]m=\frac{-4+9}{-10+5}[/tex]
[tex]m=\frac{5}{-5}[/tex]
Apply fraction rule: [tex]\frac{a}{-b}=-\frac{a}{b}[/tex]
[tex]m=-\frac{5}{5}[/tex]
[tex]m=-1[/tex]
Therefore, we verified that the slope of the line containing the points (-5, -9) and (-10, -4) is indeed m = -1.
