Question

if a line has an x-intercept at (x = -6) and a y-intercept at (y = -9), find its equation in the form (y = mx + b).

(y =)

Explanation:

Identify the given intercepts as coordinate points

The x-intercept is at \(x = -6\), which corresponds to the point \((-6, 0)\).
The y-intercept is at \(y = -9\), which corresponds to the point \((0, -9)\).

Calculate the slope of the line

Using the slope formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\):

$$ m = \frac{-9 - 0}{0 - (-6)} = \frac{-9}{6} = -\frac{3}{2} $$

Write the equation in slope-intercept form

The slope-intercept form is \(y = mx + b\), where \(b\) is the y-intercept (\(b = -9\)):

$$ y = -\frac{3}{2}x - 9 $$

Answer:

If a line has an x-intercept at \(x = -6\) and a y-intercept at \(y = -9\), find its equation in the form \(y = mx + b\).

\(y =\) <blank>\(-\frac{3}{2}x - 9\)</blank>