Question

rite the equation of a line that passes through the points (3, 10) and (-2, -20).

Answer 1

To find the equation of the line that passes through the points \((3, 10)\) and \((-2, -20)\), we can follow these steps:

1. **Calculate the slope (m)** using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Assign \((x_1, y_1) = (3, 10)\) and \((x_2, y_2) = (-2, -20)\).

\[
m = \frac{-20 - 10}{-2 - 3} = \frac{-30}{-5} = 6
\]

2. **Use the point-slope form of the equation**:
The point-slope form is given by:
\[
y - y_1 = m(x - x_1)
\]
Using point \((3, 10)\) and slope \(m = 6\):
\[
y - 10 = 6(x - 3)
\]

3. **Simplify the equation**:
\[
y - 10 = 6x - 18
\]
\[
y = 6x - 8
\]

Thus, the equation of the line that passes through the points \((3, 10)\) and \((-2, -20)\) is
\[
\boxed{y = 6x - 8}
\]