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Table of Contents
• 5.1: Understanding Linear Functions
• 5.2: Using Intercepts
• 5.3: Interpreting Rates of Change and Slope
• 6.1: Slope-Intercept Form
• 6.2: Point-Slope Form
• 6.3: Standard Form
• 6.4 Transforming Linear Functions
• 6.5: Comparing Properties of Linear Functions
Standard Form
A linear equation is any equation that can be written in the standard from:
Ax +By = C,where A, B and C are real numbers and A and B are both not 0.
5.2: Using Intercepts
Essential Questions: How can you identify and use intercepts in linear relationships?
Page: 211
Vocab: Intercepts
X-intercept: y-coordinate of the point where the graph intercepts the y-axis. The x-coordinate of this point is always zero.
Y-intercept: x- coordinate of the point where the graph intercepts the x-axis. The y-coordinate of the point is always zero.
Find the Intercepts
• To find x-intercept, replace y with zero and solve for x.
• To find y-intercept, replace x with zero and solve for y.
5.3: Interpreting Rate of Change and Slope
Essential Question: How can you relate rate of change and slope in a linear equation?
What is Slope?
• Slope: describes the steepness or incline of a line. A higher slope value indicates a steeper incline.
• Slopes can be positive, negative, zero or undefined.
• Slope is abbreviated with “m”
Determining Slope Graphically
• We can count the rise and run on a graph to determine slope.
6.1: Slope Intercept Form
Essential Question: How can you represent a linear function in a way that
reveals in slopes and y-intercept?
Lesson 6.2: Point-Slope Form
Essential Question: How can you represent a linear equation in a way that it reveals its point and slope on
its graph?
Pg. 249
Write the Point-Slope Equation
1. Slope is 3.5 and (-3, 2) is on the line.
2. Slope is 0 and (-2, -1) is on the line.
Using Point-Slope…Solve
Paul wants to place an ad in a newspaper. The newspaper charges $10 for the first 2 lines of text and $3 for each additional line of text. Paul’s is 8 lines long. How much will the ad cost?
Paul would like to shop for the best price to place the ad. A different newspaper has a base cost of $15 for 3 lines and $2 for every extra line. How much will an 8-line ad cost in this paper?
Using Point-Slope…Solve
Lesson 6.3: Standard Form
Essential Question: How can you write a linear equation in Standard Form given properties of the
line including its slopes and points on the line?
Pg. 261
Modeling: Write an Equation in Standard Form
A tank is filling up with water at a rate of 3 gallons per minute. The tank already had 3 gallons in it before it started being filled.
Modeling: Write an Equation in Standard Form
A hot tub filled with 440 gallons of water is being drained. After 1.5 hours, the amount of water had decreased to 320 gallons.
Lesson 6.4: Transforming Linear
Functions
Essential Question: What are the ways in which you can transform the
graph of a linear function?
What happens when….
A. The gym lowers the one time fee to join?
B. The gym increased the monthly fee?
Lesson 6.5: Comparing Properties of Linear
Functions
Essential Question: How can you compare linear functions that are
represented in different ways?
Comparing 2 FunctionsThe domain of each function is the set of all real numbers x such that 5≤x≤8. The table show some ordered pairs for f(x). The function g(x) is defined by the rule g(x) = 3x + 7.
What is the f(x) function rule?
f(x) initial value?
g(x) initial value?
f(x) range?
g(x) range?
Comparing 2 FunctionsThe domain of each function is the set of all real numbers x such that 6≤x≤10. The table show some ordered pairs for f(x). The function g(x) is defined by the rule g(x) = 5x + 11.
What is the f(x) function rule?
f(x) initial value?
g(x) initial value?
f(x) range?
g(x) range?
Write a function rule for each, and then compare their domain, range, slope and y-intercept.
A rainstorm in Austin lasted 3.5 hours, during which time it rained at a steady rate of 4.5 mm per hour.
The graph shows the amount of rain that dell during the same rainstorm in Dallas, D(t) as a function of time.
Austin Dallas
Function Rule
Domain
Range
Slope
Y-intercept
Write a function rule for each, and then compare their domain, range, slope and y-intercept.
The first group of hikers hiked at steady rate of 6.5 km per hour for 4 hours.
The graph shows the 2nd group of hikers.
1st Group 2nd Group
Function Rule
Domain
Range
Slope
Y-intercept