University:
High School
Course:
High School Algebra
Academic year:

2021
Views:

234

Pages:

2
Author:

Mohammad Hood

Interpret linear functions and use to model applications 1.3 Modeling with Linear Functions A. VOCABULARY & CONCEPTS Slope: Describes the steepness of a linear function. [m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{RISE}{RUN}] Slope-Intercept Form: [y=mx+b] Where M=slope and B=y-intercept B. WRITING EQUATIONS OF LINEAR FUNCTIONS In Exercises 1-3, use the graph to write an equation of the line and interpret the slope. 1. 1 1. Cell Phone Costs [m=\frac{rise}{run}=\frac{1}{10}] or [m=\frac{51-50}{10-0}=\frac{1}{10}] graph showing a line with points (0, 50) and (10, 51) [b=50] [y=\frac{1}{10}x+50] or [y=0.1x+50] Interpret Slope: Every 10 text messages costs $1. 10 cents per text message 2. Travel Distance [m=\frac{-360}{6}=-60] graph showing a line with points (0, 360) and (6, 0) [b=360] [y=-60x+360] Interpret Slope: The travel distance decreases by 60 miles for every hour traveled. Math Homework Grade [m=\frac{95-85}{20-10}=\frac{10}{10}=1] The math homework grade increases 1% for every one completed assignment. graph showing a line with points (10, 85) and (20, 95) [y=1x+b] To find b: plug in (x,y) [85=1(10)+b] [85=10+b] [75=b] [y=x+75] Table | Completed Assignments (x) | Homework Grade (y) | |---|---| | 10 | 85 | | 20 | 95 | 4. The cost of parking in a parking garage in Chicago is represented by the equation (y=15x+20) where y is the total cost (in dollars) and x is the time (in hours). The table 1 shows the total cost to park in a parking garage in Denver. Which city's parking garage charges more per hour and by how much more? After how many hours would parking 2 in both cities cost the same? 3 DENVER | Hours, x | Cost, y | |---|---| | 1 | 27 | | 2 | 35 | | 3 | 43 | | 4 | 51 | | 5 | 59 | | 6 | 67 | CHICAGO [y=15x+20] $15 per hour work backwards | Hours, x | Cost, y | | 0 | 20 | | 1 | 35 | | 2 | 50 | | 3 | 65 | Chicago charges more per hour by $7. After 1 hour parking in both cities costs the same.