The given equation is:

$y = -\frac{1}{2}x + 4$

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

• The slope $m = -\frac{1}{2}$, and
• The y-intercept $b = 4$ (the point where the line crosses the y-axis).

Now let's analyze the graphs:

• The slope $m = -\frac{1}{2}$ means that for every 2 units you move horizontally to the right (positive x-direction), the graph will drop by 1 unit (negative y-direction). So, the line should go down as you move to the right.
• The y-intercept $b = 4$ means that the line will cross the y-axis at $y = 4$.

Looking at the three graphs:

• Graph A has a line that rises, not falls, from left to right, so it doesn't match the slope.
• Graph B has a line that falls from left to right and crosses the y-axis at $y = 4$, which matches the given equation.
• Graph C has a line that rises from left to right and does not match the slope.

Therefore, Graph B is the correct representation of the equation.

Let me know if you would like more explanation or have further questions!

Here are 5 related questions to expand on:

1. How do you calculate the slope of a line given two points?
2. How do you convert a linear equation from standard form to slope-intercept form?
3. What is the significance of the y-intercept in real-life scenarios?
4. How does the slope relate to the speed of change in a situation?
5. How can you graph a linear equation without using a graphing calculator?

Tip: Always remember that the slope is the rate of change between the x and y values, and the y-intercept gives you the starting point of the graph when x is 0.