Question

write the equation of the line in fully simplified slope-intercept form.

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through the points \((-10, 9)\) and \((0, -3)\) (the y - intercept is at \((0, -3)\)).

Step2: Calculate the slope (\(m\))

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(-10,9)\) and \((x_2,y_2)=(0, - 3)\). Then \(m=\frac{-3 - 9}{0-(-10)}=\frac{-12}{10}=-\frac{6}{5}\).

Step3: Determine the y - intercept (\(b\))

The slope - intercept form of a line is \(y = mx + b\), where \(b\) is the y - intercept. We know that the line crosses the y - axis at \((0,-3)\), so \(b=-3\).

Step4: Write the equation in slope - intercept form

Substitute \(m =-\frac{6}{5}\) and \(b = - 3\) into the slope - intercept form \(y=mx + b\). We get \(y=-\frac{6}{5}x-3\).

Answer:

\(y = -\frac{6}{5}x - 3\)