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 \((-2, 0)\) and \((0, -2)\).

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

The formula for slope is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(-2,0)\) and \((x_2,y_2)=(0, - 2)\). Then \(m=\frac{-2 - 0}{0-(-2)}=\frac{-2}{2}=- 1\).

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

The y - intercept is the value of \(y\) when \(x = 0\). From the point \((0,-2)\), we can see that \(b=-2\).

Step4: Write the equation in slope - intercept form (\(y=mx + b\))

Substitute \(m=-1\) and \(b = - 2\) into the slope - intercept form. We get \(y=-x - 2\).

Answer:

\(y=-x - 2\)