Solve each problem. See Example 7 The weight y (in pounds)...

Solve each problem. See Example 7 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 nearest inch.

Solve each problem. See Example 7
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 nearest inch.

Key Concepts

Linear Equation

A linear equation represents a relationship between two variables where the rate of change is constant. It is typically expressed in the form y = mx + b, where m indicates the slope, and b represents the y-intercept. This form is fundamental in modeling situations with a steady, proportional relationship between the two quantities.

Slope-Intercept Form

The slope-intercept form of a linear equation (y = mx + b) provides a clear interpretation of the line's characteristics: the slope (m), which determines the steepness and direction, and the y-intercept (b), which is the point where the line crosses the y-axis. This form is widely used because it simplifies understanding and graphing linear relationships.

Ordered Pairs

Ordered pairs, typically in the form (x, y), represent specific coordinates on the Cartesian coordinate plane. They are essential for mapping points that satisfy a given equation, thereby allowing one to visually represent the relationship between variables in a graph.

Graphing Linear Functions

Graphing linear functions involves plotting the ordered pairs derived from a linear equation and drawing a straight line through these points. This method is useful to visualize the entire set of solutions to the equation and to intuitively understand the relationship between the variables.

Estimation Using Graphs

Estimation using graphs involves reading the plotted line to predict or determine approximate values of one variable corresponding to given values of the other variable. This approach helps to quickly assess solutions and to understand trends without needing exact calculations.

Solving Equations for a Given Variable

Solving for a given variable in an equation involves algebraic manipulation to isolate the target variable, often by using inverse operations. This technique is central in problems where, given one variable's value, one needs to determine the corresponding value of another variable using the established linear relationship.