AFM
Unit 1
Linear Basics
Linear Function: is any function that graphs to a ______________________ line. It has a ______________________ rate
of change.
General Form
Output = Initial value + Rate of change(X-input)
𝑚 = rate of change aka "slope"
𝑏 = initial value or vertical intercept or y − intercept
Examples:
1. A town of 30,000 people grows by 2000 people every year. Since the population, 𝑃, is growing at the constant rate of
2000 people per year, 𝑃, is a linear function of time, 𝑡, in years.
a) Make a table that gives the town’s population every five years of a 20 year period and graph.
b) What is the average rate of change of 𝑃 over every time interval?
c) Find the formula for 𝑃 as a function of 𝑡.
2. Mr. James wants to buy a used car for $5,000. It will depreciate to $0 worth over a 5 year period.
a) Make a table and graph showing the value of the car over the 5 year period.
b) Give a formula for the value of the car as a function of time.
AFM
Unit 1
Tables of Linears: if the value of 𝑥 (______________________) go up by equal steps in a table, then the value of 𝑦 goes
up or down in equal steps as well.
Remember: the slope between every set of points must be _____________________________.
Examples: Do these tables represent a linear function?
1.
𝑥
𝐹(𝑥)
0
10
5
20
10
30
15
40
20
50
𝑡
𝐺(𝑡)
1
5
2
4
3
5
4
4
5
5
2.
3.
𝑥
𝐹(𝑥)
0
20
10
40
20
50
30
55
𝑥
𝐹(𝑥)
-3
5
-1
1
0
-1
3
-7
4.
Ways to write a Line
𝒚 = 𝒎𝒙 + 𝒃
𝒚 − 𝒚𝟎 = 𝒎(𝒙 − 𝒙𝟎 )
𝑨𝒙 + 𝑩𝒚 = 𝑪
Examples: Recognize which form to use and how to use it
1. Consider a line running through the points (−1,4) and (3,2). Find the slope and graph it.
a) Write the equation of the line using point-slope form.
AFM
Unit 1
b) Write the equation of the line in slope-intercept form.
c) Write the equation of the line in standard form.
2. Find the equation of the line in slope intercept form which has….
a) Has x-intercept at 3 and a y-intercept at −5
b) Slope of . 1, and passes through the point (−0.1,0.02)
X-Intercept- where a graph crosses the ______________________ and all points are of the form _________________
Y-Intercept- where a graph crosses the ______________________ and all points are of the form _________________
Examples:
1. A candle is 7 inches tall after burning for 1 hour and 5 inches tall after for burning for 2 hours.
a) Write a linear equation to model the height of the candle.
b) Interpret the slope and y-intercept.
c) Find and interpret the x-intercept.
AFM
Unit 1
2. We’re throwing a Super Bowl party and have $24 to spend on soda and chips. A six-pack of soda costs $3 and a bag of
chips costs $2.
a) Find an equation relating 𝑥 and 𝑦.
b) Find the 5 possible combinations of soda/chips.
Quick Review
Horizontal line- has a slope of _____________ and its equation is __________________.
Vertical line- its slope is _____________________ and its equation is ___________________.