Sure! Let's graph the line that represents the equation:
[tex]\[
y + 2 = \frac{1}{2}(x + 2)
\][/tex]
### Step-by-Step Solution:
1. Rewrite the equation in slope-intercept form [tex]\(y = mx + b\)[/tex]:
[tex]\[
y + 2 = \frac{1}{2}(x + 2)
\][/tex]
First, distribute the [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[
y + 2 = \frac{1}{2}x + 1
\][/tex]
Next, subtract 2 from both sides to isolate [tex]\(y\)[/tex]:
[tex]\[
y = \frac{1}{2}x + 1 - 2
\][/tex]
Simplify the right side:
[tex]\[
y = \frac{1}{2}x - 1
\][/tex]
Now the equation is in the form [tex]\(y = mx + b\)[/tex] where [tex]\(m = \frac{1}{2}\)[/tex] and [tex]\(b = -1\)[/tex].
2. Identify the slope and y-intercept:
- The slope [tex]\(m\)[/tex] is [tex]\(\frac{1}{2}\)[/tex].
- The y-intercept [tex]\(b\)[/tex] is [tex]\(-1\)[/tex].
3. Plot the y-intercept on the graph:
- The y-intercept is the point where the line crosses the y-axis.
- Plot the point [tex]\((0, -1)\)[/tex].
4. Use the slope to find another point:
- The slope [tex]\(\frac{1}{2}\)[/tex] means that for every 1 unit you move to the right on the x-axis, you move [tex]\(\frac{1}{2}\)[/tex] units up on the y-axis.
- Starting from the y-intercept [tex]\((0, -1)\)[/tex], move 1 unit to the right to [tex]\((1, -1)\)[/tex] and then [tex]\(\frac{1}{2}\)[/tex] unit up to [tex]\((1, -0.5)\)[/tex].
- Plot the point [tex]\((1, -0.5)\)[/tex].
5. Draw the line:
- Use a straightedge or the line tool to draw a straight line through the points [tex]\((0, -1)\)[/tex] and [tex]\((1, -0.5)\)[/tex].
By following these steps, you can graph the line that represents the equation [tex]\(y + 2 = \frac{1}{2}(x + 2)\)[/tex].
