Question

write an equation of the line below.

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through the points \((-4, 3)\) and \((0, -1)\).

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

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(-4,3)\) and \((x_2,y_2)=(0,-1)\). Then \(m=\frac{-1 - 3}{0 - (-4)}=\frac{-4}{4}=-1\).

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

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

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

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

Answer:

\(y=-x - 1\)