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, 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 nearst 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, 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 nearst inch.

Key Concepts

Interpolation and Estimation

Interpolation is the process of estimating unknown values within the range of known data points on a graph. Estimation using a graph, especially in the context of linear functions, allows one to approximate values that may not be directly calculated using the algebraic equation.

Graphing Linear Functions

Graphing linear functions involves plotting the corresponding ordered pairs on a coordinate grid and drawing a straight line through them. This visual representation helps in interpreting the function, analyzing trends, and making estimations about values not explicitly calculated.

Solving for a Variable in Linear Equations

This concept involves manipulating a linear equation to isolate and solve for a particular variable. It is crucial when the problem requires finding one variable given the value of the other, such as determining the height corresponding to a given weight in a linear model.

Function Evaluation

Function evaluation involves substituting specific values into an equation to determine the corresponding outputs. In the context of linear functions, it means plugging in a value of x to obtain the corresponding y, which is an essential practice for understanding the relationship between variables.

Linear Equations

A linear equation represents a straight line when graphed and is typically written in the form y = mx + b, where m is the slope and b is the y-intercept. This concept is used to model relationships with constant rates of change and forms the basis for understanding more complex functions in algebra and calculus.

Ordered Pairs

Ordered pairs consist of two numbers that represent points on a coordinate plane in the form (x, y). They are fundamental in graphing functions, as they provide a means to plot specific input-output relationships that define the line of a linear equation.