Question

A line passes through the points (
–
6,
–
9) and (5,
–
9). Write its equation in slope-intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form.

Answer 1

To find the equation of a line in slope-intercept form (y = mx + b), we need to determine the slope \( m \) and the y-intercept \( b \) using the two given points, (-6, -9) and (5, -9).

1. **Calculate the slope (m)**:

The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points (-6, -9) and (5, -9):
\[
m = \frac{-9 - (-9)}{5 - (-6)} = \frac{-9 + 9}{5 + 6} = \frac{0}{11} = 0
\]

Since the slope is zero, this indicates that the line is horizontal.

2. **Determine the y-intercept (b)**:

Because the slope is zero, the line does not change in the y-direction. Thus, the y-coordinate is constantly -9 for all x-values. Therefore, the equation of the line is:
\[
y = -9
\]

3. **Final Equation**:

The equation of the line in slope-intercept form is:
\[
y = 0x - 9
\]

However, since the slope is zero, it is typically written simply as:
\[
y = -9
\]

This is the equation of the line passing through the given points.