In this exercise, you will use the red line for the men...

In this exercise, you will use the red line for the men shown on the scatter plot on the previous page to develop a model for the percentage of never-married American males ages 25–29. a. Use the two points whose coordinates are shown by the voice balloons to find the point-slope form of the equation of the line that models the percentage of never-married American males ages $25-29, y, x$ years after $1980 .$ b. Write the equation from part (a) in slope-intercept form. Use function notation. c. Use the linear function to predict the percentage of never-married American males, ages $25-29,$ in 2015 .

In this exercise, you will use the red line for the men shown on the scatter plot on the previous page to develop a model for the percentage of never-married American males ages 25–29.
a. Use the two points whose coordinates are shown by the voice balloons to find the point-slope form of the equation of the line that models the percentage of never-married American males ages $25-29, y, x$ years after $1980 .$
b. Write the equation from part (a) in slope-intercept form. Use function notation.
c. Use the linear function to predict the percentage of never-married American males, ages $25-29,$ in 2015 .

Key Concepts

Point-Slope Form

The point-slope form of a line is used to write the equation of a line when a point on the line and the slope are known. It is typically written as y - y? = m(x - x?), where (x?, y?) is a known point on the line and m is the slope. This form is particularly useful in developing a model from given data points in linear relationships.

Slope-Intercept Form

The slope-intercept form of a linear equation is written as y = mx + b, where m is the slope and b is the y-intercept. This form is convenient because it provides direct insight into how the dependent variable changes with respect to the independent variable, and it is easy to use for graphing and interpretation.

Linear Modeling

Linear modeling involves using a straight line to represent the relationship between two variables. By using two data points to calculate the slope and intercept, we can create a model that approximates the trend in the data and enables us to make predictions about future values.

Function Notation

Function notation, typically written as f(x), is a concise way to represent a relationship where each input x is associated with a unique output f(x). This notation is useful in mathematical modeling as it clearly defines the relationship and allows for easier evaluation of the function at specific values.

Data Prediction

Data prediction in the context of linear models involves using the established linear equation to estimate the value of the dependent variable for a given value of the independent variable. This process relies on extending the trend observed in the data to predict future or missing data points.

Transcript

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