(See Exercise 77 . ) The upper limit of the target heart...

(See Exercise $77 .$ ) The upper limit of the target heart rate zone can be approximated by the linear equation $$ y=-0.85 x+187 $$ where $x$ represents age and $y$ represents heartbeats per minute. (a) Complete the table of values for this linear equation. (b) Write the data from the table of values as ordered pairs. (c) Make a scatter diagram of the data. Describe the pattern indicated by the data.

(See Exercise $77 .$ ) The upper limit of the target heart rate zone can be approximated by the linear equation
$$
y=-0.85 x+187
$$
where $x$ represents age and $y$ represents heartbeats per minute.
(a) Complete the table of values for this linear equation.
(b) Write the data from the table of values as ordered pairs.
(c) Make a scatter diagram of the data. Describe the pattern indicated by the data.

Key Concepts

Scatter Diagram

A scatter diagram is a type of graph that plots ordered pairs on a coordinate plane to visually represent the relationship between two variables. It is useful for identifying patterns, trends, and potential correlations in the dataset.

Data Trend Pattern

The trend pattern in a scatter diagram refers to the general direction or relationship indicated by the plotted points. In the case of a linear model, the data points typically form a line or scatter near a line, which can show a positive, negative, or neutral correlation, depending on the slope of the line.

Ordered Pairs

Ordered pairs are a method of representing the relationship between two variables by pairing each input value with its corresponding output value in the format (x, y). This notation provides a clear and concise way to depict points in a two-dimensional coordinate system.

Independent and Dependent Variables

In any mathematical model, the independent variable is the one that is manipulated or chosen freely (commonly represented on the x-axis), while the dependent variable is the outcome or response (represented on the y-axis) that changes as a result of modifications in the independent variable.

Linear Equation

A linear equation establishes a straight-line relationship between two variables, showcasing a constant rate of change. The general form is y = mx + b, where m signifies the slope, indicating the rate of change, and b represents the y-intercept, which is the value of y when x is zero.

Table of Values

A table of values is a systematic organization of input-output pairs for a given function. It allows for the substitution of specific values for the independent variable and computing the corresponding outputs, which aids in understanding the behavior of the function.

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