Part A: To get an equation into standard form to represent the total amount rented (y) that Marguerite has to pay for renting the truck for x amount of days, we use the formula for the equation of a straight line.
Remember that the equation of a straight line passing through points is ( x_{1} , y_{1} ) and the points ( x_{2} , y_{2} ) is given by y - y_{1} / x - x_{1} = y - y_{2} / x - x_{2}
Knowing that Marguerite rented a truck at $125 for 2 days, we know if she rents the exact same truck for 5 days, she has to pay a total of $275 for the rent. <span> This means that the line modeling this situation crosses points at (2, 125) and (5, 275). </span> The equation modeling <span>the total rent (y) that Marguerite has to pay for renting the truck for x days is given by </span><span> y - 125 / x - 2 = 275 - 125 / 5 - 2 = 150 / 3 = 50 </span> But if you are writing the equation in standard form it would be <span> </span><span> 50x - y = -25
Part B: When writing the function using function notation it means you are making y the subject of the formula and then replacing the y with f(x). </span> If you remember that from part A, we have that the equation for the total rent which is y that Marguerite has to pay for renting the truck for x amount of days is given by y = 50x + 25.<span> </span><span> Writing the equation using the function notation would give us this f(x) = 50x + 25
Part C: To graph the function, we name the x-axis the number of days and name the y-axis total rent. The x-axis is numbered using the intervals of 1 while the y-axis is numbered using the intervals of 50. The points of </span>(2,125) and of (5,275) are marked on the coordinate axis and a straight line is drawn to pass through these two points.
