Question

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

Explanation:

Step1: Identify two points on the line

From the graph, the line passes through \((-4, 3)\) and \((-1, -1)\).

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 \((x_2,y_2)=(-1,-1)\). Then \(m=\frac{-1 - 3}{-1 - (-4)}=\frac{-4}{3}=-\frac{4}{3}\).

Step3: Use point - slope form \(y - y_1=m(x - x_1)\)

Using the point \((-4,3)\) and \(m = -\frac{4}{3}\), we have \(y - 3=-\frac{4}{3}(x + 4)\).

Step4: Simplify to slope - intercept form

$$
LATEXBLOCK0
$$

Or we can write it in standard form \(4x + 3y=-7\) (by multiplying both sides by 3: \(3y=-4x - 7\), then \(4x+3y=-7\)). But the slope - intercept form is also correct.

Answer:

\(y = -\frac{4}{3}x-\frac{7}{3}\) (or \(4x + 3y=-7\))