Question

write the equation of this line in slope - intercept form.
write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through the points \((0, -3)\) (the y-intercept) and \((-1, 0)\).

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

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0, - 3)\) and \((x_2,y_2)=(-1,0)\). Then \(m=\frac{0 - (-3)}{-1 - 0}=\frac{3}{-1}=- 3\).

Step3: Write the equation in slope - intercept form (\(y = mx + b\))

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

Answer:

\(y = - 3x-3\)