Question

////////HELP 50 POINTS////////

Part A: Marguerite rented a truck at $125 for 2 days. If she rents the same truck for 5 days, she has to pay a total rent of $275.

Write an equation in the standard form to represent the total rent (y) that Marguerite has to pay for renting the truck for x days.

Part B: Write the equation obtained in Part A using function notation.

Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals.

Answer 1

Think in terms of a linear function whose graph (a straight line) goes thru the 2 points given:

(2 days, $125) and (5 days, $275 ).

Find the equation of this line.
$275-$125 $150
The slope is m = ------------------------ = --------------- = $50/day
5 days - 2 days 3 days

Use the slope-intercept form of the equation of a str. line next:

y=mx + b becomes $275 = ($50/day)(5 days) + b.

Solving for b: $275 - $250 = b = $25

Thus, the equation of this line is y = ($50/day)x + $25, where that $25 is the upfront charge (y-intercept).

We must change this into standard form. To do this, group all the terms on one side. I choose to do that on the right side, so that the x term will be + .

($50/day)x - 1y + $25 = 0 is the equation of this line in std. form.

Part B: writing this equation in function notation:

y = ($50/day)x + $25 becomes f(x) = ($50/day)x + $25

Part C: To graph this equation, plot the two points on the graph:

(2, $125) and (5, $275) ... and draw a straight line thru them.

Alternatively, let x = 0 in f(x) = ($50/day)x + $25 to find the y-intercept; it is (0, $25).

Next, let f(x) = y = 0 = ($50/day)x + $25 to find the x-intercept:
-$25
50x + 25 = 0 => x = -------------- = (-1/2) day
$50/day

The x-intercept is ([-1/2] day, $0).

Of course, x must be zero or greater, as a negative number of days would be meaningless.