Solve each problem. A gas station is selling gasoline for ...

Solve each problem. A gas station is selling gasoline for $\$ 3.50$ per gallon and charges $\$ 7$ for a car wash. The cost $y$ in dollars for $x$ gallons of gasoline and a car wash is given by $$ y=3.50 x+7 $$ (a) What is the costy in dollars for 9 gallons of gasoline and a car wash? For 4 gallons of gasoline and car wash? (b) Find the number of gallons of gasoline $x$ if the cost for gasoline and a car wash is $\$ 35 .$ (c) Write the information from parts (a) and (b) as three ordered pairs. (d) Use the data from part (c) to graph the equation.

Solve each problem.
A gas station is selling gasoline for $\$ 3.50$ per gallon and charges $\$ 7$ for a car wash. The
cost $y$ in dollars for $x$ gallons of gasoline and a car wash is given by
$$
y=3.50 x+7
$$
(a) What is the costy in dollars for 9 gallons of gasoline and a car wash? For 4 gallons
of gasoline and car wash?
(b) Find the number of gallons of gasoline $x$ if the cost for gasoline and a car wash is $\$ 35 .$
(c) Write the information from parts (a) and (b) as three ordered pairs.
(d) Use the data from part (c) to graph the equation.

Key Concepts

Ordered Pairs

Ordered pairs are a way of representing data points in the coordinate plane, typically written as (x, y). They capture the relationship between two quantities and are useful for mapping and visualizing functions or equations.

Graphing Linear Equations

Graphing involves plotting several ordered pairs on the coordinate plane and drawing a straight line through them to visually represent the linear relationship given by the equation. It helps in understanding the behavior of the linear function across different values.

Solving Linear Equations

This concept involves manipulating a linear equation algebraically to isolate the unknown variable and find its value when the output is known. It is a critical skill in determining the necessary input for a desired outcome.

Function Evaluation

Function evaluation is the process of substituting a specific input value (x) into a function to calculate the corresponding output (y). This is essential in finding the exact cost or output when a particular quantity is given.

Linear Equations

A linear equation represents a straight-line relationship between two variables, typically in the form y = mx + b, where m represents the slope (rate of change) and b represents the y-intercept (the constant term). This form is fundamental to modeling and solving problems that involve a constant rate of change.

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