To graph the equation $y = \frac{1}{2}x + 5$, follow these steps:

1. Identify the slope and y-intercept:

   • The equation $y = \frac{1}{2}x + 5$ is in slope-intercept form $y = mx + b$, where:
     • $m = \frac{1}{2}$ (slope)
     • $b = 5$ (y-intercept)

2. Plot the y-intercept:

   • Start by plotting the point $(0, 5)$ on the y-axis, since $b = 5$.

3. Use the slope to find another point:

   • The slope $\frac{1}{2}$ means "rise over run." Move up 1 unit and right 2 units from $(0, 5)$ to reach the point $(2, 6)$.
   • You can also go down 1 unit and left 2 units to find another point, $(-2, 4)$.

4. Draw the line:

   • Connect the points with a straight line extending in both directions.

This line represents the equation $y = \frac{1}{2}x + 5$.

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Here are some related questions to explore:

1. What does the slope $\frac{1}{2}$ represent in real-world terms?
2. How would the graph change if the y-intercept were a negative value?
3. What if the slope were doubled? How would that affect the line's steepness?
4. How do we determine if two lines are parallel or perpendicular based on their equations?
5. How would this line look if graphed on the x-axis instead?

Tip: When graphing linear equations, always plot the y-intercept first and use the slope to find additional points.