Question

a line passes through the points (-7, 16) and (14, 4). write its equation in slope-intercept form. write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Calculate the slope

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1, y_1) = (-7, 16)$ and $(x_2, y_2) = (14, 4)$. Then $m = \frac{4 - 16}{14 - (-7)} = \frac{-12}{21} = -\frac{4}{7}$.

Step2: Use point - slope form to find the equation

The point - slope form is $y - y_1 = m(x - x_1)$. Using the point $(-7, 16)$ and $m = -\frac{4}{7}$, we have $y - 16 = -\frac{4}{7}(x + 7)$.

Step3: Simplify to slope - intercept form

Expand the right - hand side: $y - 16 = -\frac{4}{7}x - 4$. Then add 16 to both sides: $y = -\frac{4}{7}x + 12$.

Answer:

$y = -\frac{4}{7}x + 12$