Question

use the labeled point to write a point - slope form for the line.
the point - slope form of the line is
(type an equation )

Explanation:

Step1: Identify the labeled point

From the graph, the labeled point is \((-2, 1)\).

Step2: Find the slope

We can find another point on the line, say \((-1, -1)\) (by looking at the graph). The slope \(m\) is calculated as \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-1 - 1}{-1 - (-2)}=\frac{-2}{1}=- 2\).

Step3: Write the point - slope form

The point - slope form of a line is \(y - y_1=m(x - x_1)\), where \((x_1,y_1)\) is a point on the line and \(m\) is the slope. Substituting \(x_1=-2\), \(y_1 = 1\) and \(m=-2\) into the formula, we get \(y - 1=-2(x + 2)\) (since \(x-(-2)=x + 2\)).

Answer:

\(y - 1=-2(x + 2)\)