Part a)
The diagonal line goes through (0,15) and (2,20)
Find the slope based on those points
[tex](x_1,y_1) = (0,15) \text{ and } (x_2,y_2) = (2,20)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{20 - 15}{2 - 0}\\\\m = \frac{5}{2}\\\\m = 2.5\\\\[/tex]
The y intercept is b = 15 because this is where the line crosses the y axis.
We go from y = mx+b to y = 2.5x+15.
Now plug in x = 1 to find the cost of renting for one day.
y = 2.5x+15
y = 2.5*1+15
y = 17.5
Another way to get the answer is to start at 1 on the x axis number line. Draw a vertical line upward until you reach the curve. From there, draw a horizontal line toward the y axis (refer to the diagram below). You should land somewhere between 15 and 20. The midpoint of which is 17.50
Answer: $17.50
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Part b)
We can do the reverse idea of the previous part.
Start at y = 25 on the y axis. Draw a horizontal line toward the curve. After reaching the curve, draw a vertical line down until you hit the x axis. You should arrive at x = 4.
Or you can use the algebraic approach since we know the cost equation
y = 2.5x+15
25 = 2.5x+15 ... plug in y = 25
25-15 = 2.5x
10 = 2.5x
2.5x = 10
x = 10/(2.5)
x = 4
Answer: 4 days
