Americans are getting married later in life, or not getting...

Americans are getting married later in life, or not getting married at all. In 2010 , more than half of Americans ages 25 through 29 were unmarried. The bar graph shows the percentage of never-married men and women in this age group for four selected years. The data are displayed as two sets of four points each, one scatter plot for the percentage of never-married American men and one for the percentage of never-married American women. Also shown for each scater plot is a line that passes through or near the four points Use these lines to solve (figure can't copy) In this exercise, you will use the blue line for the women shown on the scatter plot to develop a model for the percentage of never-married American females 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 females 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 nevermarried American females, ages $25-29,$ in 2020

Americans are getting married later in life, or not getting married at all. In 2010 , more than half of Americans ages 25 through 29 were unmarried. The bar graph shows the percentage of never-married men and women in this age group for four selected years. The data are displayed as two sets of four points each, one scatter plot for the percentage of never-married American men and one for the percentage of never-married American women. Also shown for each scater plot is a line that passes through or near the four points Use these lines to solve (figure can't copy)
In this exercise, you will use the blue line for the women shown on the scatter plot to develop a model for the percentage of never-married American females 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 females 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 nevermarried American females, ages $25-29,$ in 2020

Key Concepts

Linear Modeling

Linear modeling involves using a straight line to approximate or describe the relationship between two variables. In many real-world scenarios, such as analyzing trends over time, a linear model can help simplify complex data into a computable function that allows predictions and insights.

Point-Slope Form

The point-slope form is a method of writing the equation of a line when a point on the line and the slope are known. It is formulated as y - y? = m(x - x?), providing a straightforward way to represent linear relationships based on initial data points.

Slope-Intercept Form

The slope-intercept form expresses a linear equation as y = mx + b, where m represents the slope and b represents the y-intercept. This form is widely used because it clearly shows how changes in the independent variable affect the dependent variable, making it ideal for graphing and interpretation.

Function Notation

Function notation, such as f(x), is a concise way to represent a function and its rule of correspondence between inputs and outputs. It allows for easy evaluation and manipulation of functions within modeling and analysis, framing the relationship in mathematical terms for predictions.

Predictive Analysis

Predictive analysis uses the established linear model to forecast future outcomes based on current data. Once a model is built, it can be utilized to estimate or predict values beyond the initial data set, offering valuable insights into trends and future behavior.

Transcript

00:03 Okay, great, seven.

00:06 They give you the two points.

00:08 They want you to use 20 and 3, 8 .9, 30, and 47 .8.

00:18 And so the ones in the bubble.

00:20 And they tell you that in the problem.

00:23 47.

00:24 So these are your two points.

00:26 So i'll go ahead and label them.

00:27 X1, y, 1, x2, y2.

00:32 And you're going to first find a slope between these two points.

00:39 So you use your slope.

00:40 Formula y2 minus y1 over x2 minus x1 equals and you just plug this in y2 minus y1 over x2 minus x1 and you should get 8 .9 over 10 or 0 .89 for your slate and you're going to put it into point slope form so what you want to do is let's look at points with slope form and that is y minus y1 equals m times x minus x1 so what you're going to do is you're going to take the slope that you just found em equals 0 .89 and one of these points from the original the ones they gave you and i used the one that's already labeled x1 and y1 it just fits between but you can all you can use these on the right side too either one will work so my y1 is 38 .9 so i'd have y minus 38 .9 equals 0 .89 times x minus 20 and it will work it will work the same for you you know you get to the right place using 4 .7 .8 and 30 in place of the ones i used.

02:13 Either point you can use.

02:16 So this is the point slope one.

02:20 Okay so now for part b we're going to take this points like 1 8 .9 .8 .9 times x minus 20 and we're going to solve it for why.

02:47 All we're going to do is add the 38 .9 both sides.

02:52 I'm sorry, distribute first.

02:58 She'd get 0 .899x minus 17 .8.

03:03 It's a good looking 7.

03:04 Sorry.

03:06 And then you'll add the 38 .9 both sides, plus 38 .9...