The bar graph shows the rise in the percentage of births to...

The bar graph shows the rise in the percentage of births to U.S. unmarried women from 1960 through 2009. a. Shown to the right of the bar graph is a scatter plot with a line passing through two of the data points. Use the two points whose coordinates are shown by the voice balloons to write the slope-intercept form of an equation that models the percentage of births to unmarried women, $y,$ in the United States $x$ years after 1960. b. If trends shown by the data continue, use the model from part (a) to project the percentage of births to unmarried women in the United States in 2020. (THE GRAPH CANNOT COPY)

The bar graph shows the rise in the percentage of births to U.S. unmarried women from 1960 through 2009.
a. Shown to the right of the bar graph is a scatter plot with a line passing through two of the data points. Use the two points whose coordinates are shown by the voice balloons to write the slope-intercept form of an equation that models the percentage of births to unmarried women, $y,$ in the United States $x$ years after 1960.
b. If trends shown by the data continue, use the model from part (a) to project the percentage of births to unmarried women in the United States in 2020.
(THE GRAPH CANNOT COPY)

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Key Concepts

Slope-Intercept Form

The slope-intercept form is an equation of a line written as y = mx + b, where m represents the slope of the line, indicating its steepness and direction, and b represents the y-intercept, which is the value of y when x is 0. This form is fundamental in linear equations and modeling relationships between two variables.

Linear Modeling

Linear modeling involves representing the relationship between two variables with a straight line. By identifying key data points, one can derive a linear equation that approximates the trend within the data, allowing for analysis and prediction. This technique is widely used in various fields to understand and forecast behaviors.

Extrapolation

Extrapolation is the process of estimating values beyond the range of the observed data using an established model or trend. When applying a linear model to predict future outcomes, it is assumed that the trend continues consistently outside the known data, though caution is necessary as conditions may change.

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