Solve each problem. The weight y (in pounds) of a man taller...

Solve each problem. The weight $y$ (in pounds) of a man taller than 60 in. can be approximated by the linear equation $$ y=5.5 x-220 $$ where $x$ is the height of the man in inches. (a) Use the equation to approximate the weights of men whose heights are 62 in., 66 in., and 72 in. (b) Write the information from part (a) as three ordered pairs. (c) Graph the equation for $x \geq 62$, using the data from part (b). (d) Use the graph to estimate the height of a man who weighs 155 lb. Then use the equation to find the height of this man to the nearest inch.

Solve each problem.
The weight $y$ (in pounds) of a man taller than 60 in. can be approximated by the linear equation
$$
y=5.5 x-220
$$
where $x$ is the height of the man in inches.
(a) Use the equation to approximate the weights of men whose heights are 62 in., 66 in., and 72 in.
(b) Write the information from part (a) as three ordered pairs.
(c) Graph the equation for $x \geq 62$, using the data from part (b).
(d) Use the graph to estimate the height of a man who weighs 155 lb. Then use the equation to find the height of this man to the nearest inch.

Key Concepts

Ordered Pairs

Ordered pairs are a way to represent a point in the Cartesian coordinate system, typically written as (x, y). They convey both the input and output of a function, allowing one to clearly see the relationship between two quantities. In the context of linear functions, ordered pairs help in organizing and displaying specific data points that lie on the straight line defined by the equation.

Linear Functions

A linear function represents a relationship between two variables with a constant rate of change. The equation is usually written in the form y = mx + b, where m is the slope that indicates how much y changes for a one-unit change in x, and b is the y-intercept, the value where the line crosses the y-axis. This concept underlies many real-world scenarios where one quantity changes at a constant rate with respect to another.

Substitution to Evaluate Functions

Substitution involves replacing the variable in an equation or function with a specific value in order to compute the corresponding output. This process is essential when using a function to approximate or predict real-world values by directly plugging in measurements and calculating the result.

Graphing Linear Equations

Graphing a linear equation involves plotting the ordered pairs on a Cartesian coordinate system and then drawing the line that passes through these points. This visual representation makes it easier to understand the relationship between the variables and can be used for making predictions, estimating values, or verifying solutions obtained algebraically.

Solving Inverse Problems in Linear Equations

Solving an inverse problem involves finding the input value that corresponds to a given output value. In the case of linear equations, this is typically done by rearranging the equation to solve for the independent variable. This technique is useful for determining the original measure that produces a particular result in a modeled relationship.

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