Let's solve and graph the given equation:

The line provided is:
$y + 5 = \frac{1}{2}(x + 6)$

Step 1: Rewrite into slope-intercept form $y = mx + b$.

1. Start with the equation:
   $y + 5 = \frac{1}{2}(x + 6)$
2. Distribute the $\frac{1}{2}$ on the right side:
   $y + 5 = \frac{1}{2}x + 3$
3. Subtract $5$ from both sides:
   $y = \frac{1}{2}x + 3 - 5$
4. Simplify:
   $y = \frac{1}{2}x - 2$

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

• Slope ($m$) = $\frac{1}{2}$
• Y-intercept ($b$) = $-2$

Step 2: Plot the line.

1. Start at the y-intercept $b = -2$. Plot the point $(0, -2)$.
2. Use the slope $\frac{1}{2}$ (rise over run):
   • From $(0, -2)$, go up 1 unit and right 2 units to reach the next point $(2, -1)$.
   • Continue this to find additional points if necessary.
3. Draw a straight line through the points.

Key Points for Graphing:

• The line passes through:
  • $(0, -2)$ (y-intercept)
  • $(2, -1)$ (using the slope).
• The slope indicates the line rises 1 unit for every 2 units to the right.

Let me know if you’d like further clarification or help plotting!

Related Questions:

1. How do you calculate slope from two points?
2. What is the significance of the y-intercept?
3. How can I convert a standard form equation into slope-intercept form?
4. What is the general process for graphing a line given its equation?
5. How can you find the x-intercept of this line?

Tip: Always simplify equations into slope-intercept form to make graphing easier!