a We have been given a linear equation and are asked to graph the line as well as find its domain and range. Since the equation is already in slope-intercept form, let's jump right into graphing. We need to identify the slope and y-intercept of the equation, c(x)=0.5x+70.
Slope:& 0.5
y-intercept:&70
We can begin graphing by plotting the y-intercept.
Next, we will use the slope to find a second point on the graph. Thinking of our slope as 12 will make it is easier to find the rise and the run. Based on the dimensions of our graph so far, it will be even easier if we think of this as 1020. Therefore, we rise 10 units as we run 20 units. Once we have second point, we can draw a line through the points.
To find the domain and range it is important to think about how many miles one can drive. We can drive zero or more miles, but we cannot drive a negative number of miles. This means that the domain is all real numbers greater than 0. The range is then all real numbers greater than $70.
Domain:&x ≥ 0
Range:& c ≥ 70
b As a unit rate, the slope is 12. This means that for every 2 miles we drive, the cost of renting a truck c increases by $1.
1/2 = $1 in truck rental fees/2 miles driven
The c-intercept tells us that the base price for renting the truck is $70.
