Question

Line p goes through points (-2,6) and (4,-3).
What is the equation of line p?

Answer 1

To find the equation of the line \( p \) that passes through the points \((-2, 6)\) and \((4, -3)\), we can start by finding the slope of the line using the slope formula:

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

Here, we can denote the points as \((x_1, y_1) = (-2, 6)\) and \((x_2, y_2) = (4, -3)\). Plugging in these coordinates:

\[
m = \frac{-3 - 6}{4 - (-2)} = \frac{-9}{4 + 2} = \frac{-9}{6} = -\frac{3}{2}
\]

Now that we have the slope \( m = -\frac{3}{2} \), we can use the point-slope form of the equation of a line, which is given by:

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

Using the point \((-2, 6)\):

\[
y - 6 = -\frac{3}{2}(x - (-2))
\]

Simplifying:

\[
y - 6 = -\frac{3}{2}(x + 2)
\]

Next, distribute the slope:

\[
y - 6 = -\frac{3}{2}x - 3
\]

Now, add 6 to both sides to solve for \( y \):

\[
y = -\frac{3}{2}x - 3 + 6
\]
\[
y = -\frac{3}{2}x + 3
\]

Therefore, the equation of line \( p \) in slope-intercept form is:

\[
\boxed{y = -\frac{3}{2}x + 3}
\]