Question

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

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through \((-7, 0)\) and \((0, -7)\).

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

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(-7,0)\) and \((x_2,y_2)=(0,-7)\). Then \(m=\frac{-7 - 0}{0 - (-7)}=\frac{-7}{7}=-1\).

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

The y - intercept is the value of \(y\) when \(x = 0\). From the point \((0,-7)\), we can see that \(b=-7\).

Step4: Write the equation in slope - intercept form

The slope - intercept form of a line is \(y=mx + b\). Substituting \(m=-1\) and \(b = - 7\) into the formula, we get \(y=-x-7\).

Answer:

\(y=-x - 7\)