Answer:
Part 1: Equation modeling y in terms of x (i.e., total charge in terms of number of miles driven: y = 0.25x + 30
Part 2: Total charge for driving 125 miles = $61.25
Explanation:
Part 1: Modeling the total charge in terms of x:
- The problem can best be modeled by a linear equation.
- Since we're told there's both a flat fee and a $0.25 fee per mile, the slope-intercept form would best model the problem.
The general equation of the slope-intercept form is given by:
y = mx + b, where
- m is the slope,
- and b is the y-intercept.
Determining the slope, m:
- The slope can be defined as the change in y / the change in x.
- We see that charge is represents the set of y values (i.e., the dependent variable) and number of miles driven represents the sex of x values (i.e., the independent variable).
Thus, the slope, m, is 0.25.
Determining the y-intercept, b:
- For any y-intercept, the x-coordinate is 0 since it's the point where a line intersects the y-axis.
- In context of the problem, the y-intercept is the amount charged by the company even when no miles are driven.
Thus, the $30 flat fee is the y-intercept, b.
Creating the equation:
Therefore, the equation that models the y (i.e., the total charge in dollars) in terms of x (i.e., the number of miles driven) is given by:
y = 0.25x + 30
Part 2: Determining the total charge from driving 125 miles:
Now we can determine the total charge of driving 125 miles by substituting 125 for x in the equation we just found:
y = 0.25(125) + 30
y = 31.25 + 30
y = 61.25
Thus, the total charge for driving 125 miles is $61.25