Question

find an equation of the line l. the equation is \boxed{}. (type an equation. simplify your answer.)

Explanation:

Step1: Identify two points on line L

From the graph, the two points are \((-4, 2)\) and \((-1, -1)\).

Step2: Calculate the slope (m)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting \(x_1=-4,y_1 = 2,x_2=-1,y_2=-1\), we get \(m=\frac{-1 - 2}{-1-(-4)}=\frac{-3}{3}=-1\).

Step3: Use point - slope form

Using point \((-4,2)\) and \(m = - 1\), the point - slope form is \(y - y_1=m(x - x_1)\). Substituting values: \(y - 2=-1(x + 4)\).

Step4: Simplify to slope - intercept form

Expand the equation: \(y-2=-x - 4\). Add 2 to both sides: \(y=-x - 2\).

Answer:

\(y=-x - 2\)