A line has a slope of -4 and includes the points $$ (-7,-4) $$ and $$ (r, 4) $$. What is the value of $$ r $$ ?

Question

UpStudy AI · Accepted Answer

To find the value of $$ r $$, we'll use the slope formula between two points on a line:

$$
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
$$

Given:
- Slope $$ m = -4 $$
- Points $$ (-7, -4) $$ and $$ (r, 4) $$

Plugging the points into the slope formula:

$$
-4 = \frac{4 - (-4)}{r - (-7)} = \frac{8}{r + 7}
$$

Now, solve for $$ r $$:

$$
-4 = \frac{8}{r + 7}
$$

Multiply both sides by $$ r + 7 $$:

$$
-4(r + 7) = 8
$$

$$
-4r - 28 = 8
$$

Add 28 to both sides:

$$
-4r = 36
$$

Divide by -4:

$$
r = -9
$$

**Answer:** $$-9$$
$$ r = -9 $$

A line has a slope of -4 and includes the points and . What is the value of ?