Question

A line passes through the points (-2,7) and (3,-8). Choose one of your equations from Part II. Rewrite your equation (from Part II) into slope-intercept form.

Answer 1

To find the equation of the line that passes through the points (-2, 7) and (3, -8), we first need to calculate the slope (m) using the slope formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Let's assign the points as follows:
- \((x_1, y_1) = (-2, 7)\)
- \((x_2, y_2) = (3, -8)\)

Now, substitute the values into the slope formula:

\[
m = \frac{-8 - 7}{3 - (-2)} = \frac{-15}{3 + 2} = \frac{-15}{5} = -3
\]

Now that we have the slope \( m = -3 \), we can use the point-slope form of the line's equation, which is given by:

\[
y - y_1 = m(x - x_1)
\]

Using the point (-2, 7):

\[
y - 7 = -3(x - (-2))
\]

This simplifies to:

\[
y - 7 = -3(x + 2)
\]

Expanding the right side:

\[
y - 7 = -3x - 6
\]

Now, add 7 to both sides to isolate \( y \):

\[
y = -3x - 6 + 7
\]
\[
y = -3x + 1
\]

Thus, the equation of the line in slope-intercept form \( (y = mx + b) \) is:

\[
\boxed{y = -3x + 1}
\]