Step-by-step explanation:
In the given problem, there are two plans that can be represented with a linear function.
Plan A:
A = total monthly cost of Plan A for every x number of movies that Sadie watches per month
Slope: $3 = The additional cost for every x number of movies watched per month
Y-intercept: $21 = The monthly cost of Plan A
Combining these elements together, we can establish the following linear function: A(x) = 3x + 21
Plan B:
B = total monthly cost of Plan B for every x number of movies that Sadie watches per month
Slope: $1.50 = The additional cost for every x number of movies watched per month
Y-intercept: $27 = The monthly cost of Plan B
Combining these elements together, we can establish the following linear function: B(x) = 1.5x + 27 or [tex]\displaystyle\mathsf{B(x)\:=\:\frac{3}{2}x\:+\:27}[/tex].
Graphing:
Plan A:
In order to graph Plan A, start with plotting the y-intercept, (0, 21). The y-intercept is the point on the graph where it crosses the y-axis. Then, use the slope, m = 3 (rise 3, run 1), to plot the other points on the graph.
Plan B:
Similarly for Plan B, start with plotting the y-intercept, (0, 27).
Then, use the [tex]\displaystyle\mathsf{slope (m)\:=\:1.5\:or\:\frac{3}{2}}[/tex] (rise 3, run 2), to plot the other points on the graph.
Attached is the graphed linear functions, A(x) and B(x). The two lines intersect at point, (4, 33), which means that the total cost of Plans A and B will be the same at $33.
Interval of movies watched:
The attached graph also shows that when 0 ≤ x < 4, Plan A is cheaper than Plan B. The interval notation is: [0, 4).
This implies that when Sadie watches 0 - 4 movies per month, she will pay lesser in Plan A than Plan B.
