The equation you're tasked with graphing is:

$y = \frac{1}{2}x + 3$

This is a linear equation in slope-intercept form, where:

• The slope $m = \frac{1}{2}$
• The y-intercept $b = 3$

Steps to graph it:

1. Plot the y-intercept: The y-intercept is $b = 3$, so place a point at $(0, 3)$ on the graph.
2. Use the slope: The slope is $\frac{1}{2}$, which means for every 2 units you move horizontally to the right (positive $x$-direction), you move 1 unit up vertically.
3. Draw the line: After plotting a second point using the slope (for example, from $(0, 3)$ move 2 units right and 1 unit up to reach $(2, 4)$), connect these points with a straight line.

This will give you the graph of the equation.

Would you like to continue with a deeper explanation or specific details on plotting?

Here are some related questions:

1. How do you interpret the slope of a linear equation?
2. What happens to the graph if the slope is negative instead of positive?
3. How can you determine the x-intercept of this equation?
4. What is the role of the y-intercept in graphing a linear equation?
5. How do you use the equation to predict values of $y$ for given $x$-coordinates?

Tip: When graphing, always start by plotting the y-intercept, then use the slope to find additional points.