Question

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

Explanation:

Step1: Identify two points

From the graph, we can see that the line passes through \((-2, 0)\) and \((0, -1)\).

Step2: Calculate the slope

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

Step3: Find the y - intercept

The y - intercept \(b\) is the value of \(y\) when \(x = 0\). From the point \((0,-1)\), we can see that \(b=-1\).

Step4: Write the equation in slope - intercept form

The slope - intercept form of a line is \(y=mx + b\). Substituting \(m =-\frac{1}{2}\) and \(b=-1\) into the formula, we get \(y=-\frac{1}{2}x-1\).

Answer:

\(y = -\frac{1}{2}x - 1\)