Question

use the drawing tools to form the correct answer on the graph.
graph the line that represents the equation:
$y + 2 = \frac{1}{2}(x + 2)$
drawing tools interface and coordinate graph as shown in the image

Explanation:

Step1: Identify the form

The equation \( y + 2=\frac{1}{2}(x + 2) \) is in point - slope form \( y - y_1=m(x - x_1) \), where \( (x_1,y_1)=(-2,-2) \) and \( m = \frac{1}{2} \).

Step2: Plot the point

First, plot the point \( (-2,-2) \) on the coordinate plane.

Step3: Use the slope

The slope \( m=\frac{1}{2} \) means for every 2 units we move to the right (increase in \( x \) by 2), we move up 1 unit (increase in \( y \) by 1). From the point \( (-2,-2) \), moving 2 units right to \( x = 0 \) and 1 unit up to \( y=-1 \), we get the point \( (0,-1) \).

Step4: Draw the line

Draw a line passing through the points \( (-2,-2) \) and \( (0,-1) \) (and other points obtained by using the slope) to represent the equation.

Answer:

The line is drawn through the points \((-2, - 2)\) and \((0, - 1)\) (and follows the slope \(\frac{1}{2}\)) on the given coordinate plane.