(3) Learn with an example of Watch a video A line passes through the points \( (2,-2) \) and \( (3,-9) \). Write its equation in slope-intercept form. White your answer using invegers, prgper nactions, and inproper mactions in sinplest form.

To find the equation of the line in slope-intercept form \(y = mx + b\), we first need to determine the slope \(m\) using the formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Plugging in our points \( (2, -2) \) and \( (3, -9) \), we get: \[ m = \frac{-9 - (-2)}{3 - 2} = \frac{-9 + 2}{1} = \frac{-7}{1} = -7 \] Now, using the point-slope form \(y - y_1 = m(x - x_1)\) with point \( (2, -2) \): \[ y - (-2) = -7(x - 2) \] Simplifying gives us: \[ y + 2 = -7x + 14 \] Thus, \[ y = -7x + 12 \] This is the slope-intercept form of the line! Converting to improper fractions, the slope is \(-\frac{7}{1}\) and the y-intercept is \(12\). In proper fractions, \(-\frac{7}{1}\) remains the same. A fun twist? The steep negative slope indicates that for every 1 unit you move right, you drop 7 units down, making it a mighty downhill ride! If we were to represent the slope as a fraction or improper fraction, it would be \(-\frac{7}{1}\). And another engaging note: the steepness of the line shows a rapid decline, almost like a roller coaster! So, buckle up for the ride down.