50 pointspart 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.

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.