Questions: A line passes through the points (-6,-9) and (5,-9). Write its equation in slope-intercept form.

Transcript text: 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.

Solution

Solution Steps

Step 1: Calculate the slope of the line

The slope $ m $ of a line passing through two points $ (x_1, y_1) $ and $ (x_2, y_2) $ is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substitute the given points $ (-6, -9) $ and $ (5, -9) $: \[ m = \frac{-9 - (-9)}{5 - (-6)} = \frac{0}{11} = 0 \]

Step 2: Determine the y-intercept

Since the slope $ m = 0 $, the line is horizontal. The equation of a horizontal line is: \[ y = b \] where $ b $ is the y-coordinate of any point on the line. Using the point $ (-6, -9) $: \[ y = -9 \]

Step 3: Write the equation in slope-intercept form

The slope-intercept form of a line is: \[ y = mx + b \] Substitute $ m = 0 $ and $ b = -9 $: \[ y = 0x - 9 \] Simplify: \[ y = -9 \]

The equation of the line is $ y = -9 $.