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

The value of j = -5

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=(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=(-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=(-4-\left(-9\right))/(-10-j)`

Multiply both sides by -10 - j

`-1\cdot \left(-10-j\right)=(5)/(-10-j)\left(-10-j\right)`

Simplify

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

Divide both sides by -1

`(-\left(-10-j\right))/(-1)=(5)/(-1)`

Simplify

`-10-j=-5`

Add 10 to both sides

`-10-j+10=-5+10`

Simplify

`-j=5`

Divide both sides by -1

`(-j)/(-1)=(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=(y_2-y_1)/(x_2-x_1)`

Here:

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

`m=(-4-\left(-9\right))/(-10-\left(-5\right))`

`m=(-4+9)/(-10+5)`

`m=(5)/(-5)`

Apply fraction rule:
`(a)/(-b)=-(a)/(b)`

`m=-(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.