The given equation is:

$y + 2 = \frac{1}{2}(x + 2)$

Let's break it down into steps to rewrite and graph the equation:

Step 1: Simplify the equation

Distribute $\frac{1}{2}$ on the right-hand side:

$y + 2 = \frac{1}{2}x + 1$

Now, isolate $y$ by subtracting $2$ from both sides:

$y = \frac{1}{2}x + 1 - 2$

Simplify further:

$y = \frac{1}{2}x - 1$

Step 2: Identify slope and y-intercept

The equation is now in slope-intercept form: $y = mx + b$, where:

• $m = \frac{1}{2}$ (slope)
• $b = -1$ (y-intercept)

Step 3: Plot the line

1. Start by plotting the y-intercept: $(-1)$ on the $y$-axis (point $(0, -1)$).
2. Use the slope $\frac{1}{2}$: rise $1$ unit up and run $2$ units to the right from the y-intercept. This gives another point, $(2, 0)$.
3. Connect these points to form the line.

Would you like further clarification on graphing or a step-by-step drawing? Here are related questions:

Related Questions:

1. How do you determine the slope from an equation in slope-intercept form?
2. What happens if the slope is negative instead of positive?
3. How do you convert an equation from point-slope form to slope-intercept form?
4. What does the y-intercept represent graphically?
5. How would you graph an equation if it’s given in standard form $Ax + By = C$?

Tip:

Always check your slope by ensuring the ratio of the vertical change to the horizontal change is consistent across points!