A line passes through the points \( (-4,17) \) and \( (3,-18) \). Write its equation in slope-intercept form. Write your answer using integers, proper fractions, and improper fractions in simplest form.

To find the equation of the line passing through the points \( (-4, 17) \) and \( (3, -18) \), we first need to find the slope \( m \). The formula for the slope between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting in our points: \[ m = \frac{-18 - 17}{3 - (-4)} = \frac{-35}{7} = -5 \] Next, we use the point-slope form of a line, which is \( y - y_1 = m(x - x_1) \). We can use either point; let's use \( (-4, 17) \): \[ y - 17 = -5(x + 4) \] Distributing: \[ y - 17 = -5x - 20 \] Adding 17 to both sides gives us: \[ y = -5x - 3 \] Thus, the equation of the line in slope-intercept form is: \[ y = -5x - 3 \]