Topic 3 - Miami-Dade County Public Schoolsteachers.dadeschools.net/sdaniel/Topic 3 Notes.pdf · Table of Contents •5.1: Understanding Linear Functions •5.2: Using Intercepts •5.3:

Topic 3Mrs. Daniel- Algebra 1

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

Lesson 5.1: Understanding Linear Functions

Essential Question: What is a linear function?

Pg. 202

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.

Discrete vs. Continuous Function

Discrete or Continuous?Domain: _______________Range: _______________

Discrete or Continuous?Domain: _______________Range: _______________

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.

Find Intercepts: -5x + 6y = 60

Graph Using the Intercepts:18y = 12x + 108

Graph Using the Intercepts:3y = -5x -3

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.

Slope

Slope Formula

Find the Slope, using the graph

Find the Slope, using the table

Slope:

Interpret:

Slope:

Interpret:

Slope:

Interpret:

Slope:

Interpret:

6.1: Slope Intercept Form

Essential Question: How can you represent a linear function in a way that

reveals in slopes and y-intercept?

Slope Intercept Form

Find the slope- intercept form

Slope is 3, and (2, 5) is on the line

Find the slope- intercept form

The line passes through (0,5) and (2,13).

Graphing the Slope Intercept Form of a Line

Graphing the Equation of a Line

1. Start at “b”.

2. Move up/down

3. Move left/right

4. Repeat

Graph: y = 5x -4

Graph: 2x + 6y = 6

Graph: 2x + 3y = 6

Graph: 2x + y = 4

Slope:

Interpret:

Y-intercept:

Interpret:

Equation:

Slope:

Interpret:

Y-intercept:

Interpret:

Equation:

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

Point Slope Equation

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

Let’s Practice…

(2, 1) and (3, 4) are on the line. Write an equation in point-slope form.

Let’s Practice…

(1, 3) and (2, 3) are on the line. Write an equation in point-slope form.

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

Comparing Forms of Linear Equations

Write in Standard Form…

Slope is 2 and (-2, 2) is on the line.

Write in Standard Form…

Slope is 5 and (-2, 4) is on the line.

Let’s Practice…

Write in Standard Form…

(-2, -1) and (0, 4) are on the line.

Write in Standard Form…

(5, 2) and (3, -6) are on the line.

Let’s Practice…

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.

Let’s Practice…

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?

Changes to… Words Visually

Slope (m)

Intercept (b)

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