For each situation, (a) write an equation in the form y=m...

For each situation, (a) write an equation in the form $y=m x+b,(b)$ find and interpret the ordered pair associated with the equation for $x=5,$ and $(c)$ answer the question. See Examples $7(b)$ and $7(c)$. A rental car costs $\$ 50$ plus $\$ 0.20$ per mile. Let $x$ represent the number of miles driven and $y$ represent the total charge to the renter. How many miles was the car driven if the renter paid $\$ 84.60 ?$

For each situation, (a) write an equation in the form $y=m x+b,(b)$ find and interpret the ordered pair associated with the equation for $x=5,$ and $(c)$ answer the question. See Examples $7(b)$ and $7(c)$.
A rental car costs $\$ 50$ plus $\$ 0.20$ per mile. Let $x$ represent the number of miles driven and $y$ represent the total charge to the renter. How many miles was the car driven if the renter paid $\$ 84.60 ?$

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Key Concepts

Linear Functions

This concept involves representing relationships where there is a constant rate of change between two variables. The relationship is typically expressed in the slope-intercept form y = m*x + b, where m represents the slope and b the y-intercept.

Interpretation of Slope and Y-Intercept

In a linear cost function, the slope (m) represents the variable cost per unit change (such as cost per mile), while the y-intercept (b) represents the fixed initial cost regardless of the unit measurement. This helps in understanding how the total cost accumulates from a base charge plus a per-unit rate.

Solving Linear Equations

This involves substituting a known value into the linear equation and isolating the unknown variable. It is a fundamental technique in algebra that permits the determination of one variable when the other variable’s value is known.

Ordered Pair and its Interpretation

An ordered pair in this context gives a specific instance of the cost function, such as the total cost at a particular number of miles driven. It illustrates the practical application of the linear model by showing the relationship between the number of miles and the total charge.

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