# How Do You Find the Equation of a Line From an Application?

Below are some problems that students solved on the board in previous semesters. All of them start from the slope-intercept form of a line and require you to find the slope m from two points and then solve for b. Click on the pictures to see a larger version.

Problem The percent p of adults who smoke cigarettes can be modeled by a linear equations p = mt + b, where t is the number of years after 1960. If two points on the graph of this function are (25, 30.7) and (50, 18.1), write the linear equation of this application.

Solution Problem The number of women in the workforce, based on data and projections from 1950 to 2050, can be modeled by a linear equation y = mx + b. The number was 18.4 million in 1950 and is projected to be 81.6 million in 2030. Let x represent the number of years after 1950 and y be the number of women in the workforce in millions.

a. What is the slope of the line through (0, 18.4) and (80,81.6)?

b. What is the average rate of change in the number of women in the workforce during this time period?

c. Use the slope from part a and the number of million of women in the workforce in 1950 to write the equation of the line.

Solution 