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 \((-1, 0)\) and \((0, -4)\).

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

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(-1,0)\) and \((x_2,y_2)=(0,-4)\). Then \(m=\frac{-4 - 0}{0 - (-1)}=\frac{-4}{1}=-4\).

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

The y - intercept is the value of \(y\) when \(x = 0\). From the point \((0,-4)\), we can see that \(b=-4\).

Step4: Write the equation in slope - intercept form

The slope - intercept form of a line is \(y=mx + b\). Substituting \(m=-4\) and \(b = - 4\) into the formula, we get \(y=-4x-4\).

Answer:

\(y = - 4x-4\)