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

To find the value of \( r \), we can use the slope formula, which is defined as: \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \] In this case, we have the slope as \(-4\), the point \((-7, -4)\) which we can consider as \((x_1, y_1)\), and the point \((r, 4)\) which is \((x_2, y_2)\). Plugging in these values into the slope formula gives: \[ -4 = \frac{4 - (-4)}{r - (-7)} \] This simplifies to: \[ -4 = \frac{4 + 4}{r + 7} \] \[ -4 = \frac{8}{r + 7} \] Next, we can cross-multiply to solve for \( r \): \[ -4(r + 7) = 8 \] Distributing \(-4\) results in: \[ -4r - 28 = 8 \] Adding \(28\) to both sides gives: \[ -4r = 36 \] Finally, dividing by \(-4\) yields: \[ r = -9 \] Thus, the value of \( r \) is \(-9\).