Question

Find the equation of the line that goes through the points (4, –1) and (2, –5).

Answer 1

To find the equation of the line that passes through the points \((4, -1)\) and \((2, -5)\), we can follow these steps:

1. **Calculate the slope (m)** using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Here, \((x_1, y_1) = (4, -1)\) and \((x_2, y_2) = (2, -5)\).

Substituting in the values:
\[
m = \frac{-5 - (-1)}{2 - 4} = \frac{-5 + 1}{2 - 4} = \frac{-4}{-2} = 2
\]

2. **Use the point-slope form of the equation**:
The point-slope form of a line is given by:
\[
y - y_1 = m(x - x_1)
\]
We can use point \((4, -1)\) and the slope \(m = 2\):
\[
y - (-1) = 2(x - 4)
\]
Simplifying this:
\[
y + 1 = 2(x - 4)
\]
\[
y + 1 = 2x - 8
\]
\[
y = 2x - 8 - 1
\]
\[
y = 2x - 9
\]

3. **Final Equation**:
The equation of the line in slope-intercept form is:
\[
y = 2x - 9
\]