Question Write the equation of the line that passes through the points \( (-9,-4) \) and \( (-5,-1) \). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

To find the equation of the line passing through points \((-9, -4)\) and \((-5, -1)\), we start by calculating the slope \(m\) using the formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Plugging in our points, we have: \[ m = \frac{-1 - (-4)}{-5 - (-9)} = \frac{-1 + 4}{-5 + 9} = \frac{3}{4} \] Now we can use the point-slope form of the line equation, which is \(y - y_1 = m(x - x_1)\). Choosing point \((-9, -4)\): \[ y - (-4) = \frac{3}{4}(x - (-9)) \] Simplifying this, we get: \[ y + 4 = \frac{3}{4}(x + 9) \] Thus, the equation of the line in point-slope form is: \[ y + 4 = \frac{3}{4}(x + 9) \] One interesting fact about lines is that they can be represented in various forms! The slope-intercept form, \(y = mx + b\), is quite popular, as it makes it easy to identify the slope and y-intercept directly. If you're ever unsure about your slope calculation, remember that it is just "rise over run"! A common mistake is to switch the coordinates for the slope formula, so double-check that you're always subtracting in the correct order: \((y_2 - y_1)\) over \((x_2 - x_1)\). That small detail makes a big difference!