If we let xdenote the number of gallons pumped, then the total cost yin dollars
can be found using the following linear equation.
Total cost Number of gallons
Theoretically, there are infinitely many ordered pairs that satisfy this equation,
but here we are limited to nonnegative values for x, since we cannot have a negative
number of gallons. In this situation, there is also a practical maximum value for xthat
varies from one car to another. What determines this maximum value?
(b)A car wash at this gas station costs an additional $3.00. Write an equation that
defines the cost of gas and a car wash.
The cost will be dollars for xgallons of gas and a car wash.
Delete unnecessary zeros.
(c) Interpret the ordered pairs and in relation to the equation from
part (b).
The ordered pair indicates that 5 gal of gas and a car wash costs $19.00.
Similarly, 1 10, 35 2 indicates that 10 gal of gas and a car wash costs $35.00.
1 5, 19 2
1 5, 19 2 1 10, 35 2
y=3.2x+ 3
3.20x+ 3.00
1 x, y 2
y= 3.20x
SECTION 3.3 Linear Equations in Two Variables 167
Number of Cost of This
Gallons Pumped Number of Gallons
0
1
2
3
4 41 $3.20 2 =$12.80
31 $3.20 2 =$9.60
21 $3.20 2 =$6.40
11 $3.20 2 =$3.20
01 $3.20 2 =$0.00
NOW TRY
NOTE In Example 7(a),the ordered pair satisfied the equation, so the linear
equation has the form where If a realistic situation involves an ini-
tial charge plus a charge per unit, as in Example 7(b),the equation has the form
where
Finding an Equation of a Line That Models Data
Average annual tuition and fees for in-state students at public two-year colleges are
shown in the table for selected years and graphed as ordered pairs of points in the
scatter diagramin FIGURE 33, where represents 2004, represents 2005,
and so on, and yrepresents the cost in dollars.
x= 0 x= 1
EXAMPLE 8
y=mx+b, bZ0.
y=mx, b=0.
1 0, 0 2
y
x
2600
2200
2300
2400
2500
2100
2000
0 152
Ye a r
34
Cost (in dollars)
FIGURE 33
Year Cost (in dollars)
2004 2079
2005 2182
2006 2266
2007 2292
2008 2372
2009 2544
Source:The College Board.
NOW TRY
EXERCISE 7
A cell phone plan costs $100
for the telephone plus $85 per
month for service. Write an
equation that gives the cost y
in dollars for xmonths of cell
phone service using this plan.
NOW TRY ANSWER
- y= 85 x+ 100