Question

If the slope of a line is -1 and two points on the line are (-9, 3) and (-10, r), what is the value of r?

Answer 1

`r=4`

Explanation:

We know that the slope of the line is -1.

We also know that the line passes through (-9, 3) and (-10, r).

We want to find the value of r.

First, let's figure out the equation of our line. We can use the point-slope form:

`y-y_1=m(x-x_1)`

Where m is the slope and (x₁, y₁) is a point.

So, let's substitute -1 for m. Since we know the point (-9, 3), let's use this for (x₁, y₁).

Substitute:

`y-(3)=-1(x-(-9))`

Simplify:

`y-3=-(x+9)`

Distribute:

`y-3=-x-9`

Add 3 to both sides. So, our equation is:

`y=-x-6`

It passes through (-10, r) and we want to find the value of r. So, let's substitute -10 for x and r for y, since -10 is our x and r is our y. So:

`r=-(-10)-6`

Evaluate for r. Distribute:

`r=10-6`

Subtract:

`r=4`

So, the value of r is 4.

And we're done!