Answer:
Points include: (0, 2); (2, 3); (4, 4)
The equation of the line is y = 1/2x + 2.
Step-by-step explanation:
The question wants you to graph the function F(n), where x is the number of additional layers added and y is the total amount of frosting. The question states that a 2-layer cake needs 2 cups of frosting and any additional layers need an extra half a cup. This means at 0 additional layers, the cake already needs 2 cups of frosting. Therefore, the b, or y-intercept (the point that "intercepts", or touches, the y-axis) is equivalent to 2. Therefore, in the slope-intercept form equation y = mx + b, where b is the y-intercept and m is the slope, b = 2. Currently, our equation looks like this: y = mx + 2.
Now, we need to find m, or the slope. We know that each additional layer needs an extra 1/2 cup of frosting, which means the slope is 1/2 since you add an extra 1/2 cup for each layer. Now, we can plug in 1/2 for m into our equation to get y = 1/2x+2.
Now, to graph, you only need 2 points. One point is the y-intercept, which we already know is (0, 2). Another one follows the slope. The slope is rise over run and is equivalent to 1/2 in this equation. This means another point on the line is one unit about (the rise) and two units to the right (the run) of (0, 2). That point would then be (2, 3).
I have attached an image of the graph below:
