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PPT – Chapter 1 Linear Functions and Mathematical Modeling Section 1.1 PowerPoint presentation | free to download - id: 6e6f34-ZWZmZ

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Chapter 1 Linear Functions and

Mathematical Modeling Section 1.1

Section 1.1Linear Equations and Intercepts

- Intercepts
- General Form of a Linear Equation
- Graphing Lines Using the Intercepts
- Interpreting Intercepts in Different Contexts

The graph of a linear equation is a straight

line. The x-intercept of the graph of a line is

the point where the line crosses the x-axis

The y-intercept of the graph of a line is the

point where the line crosses the y-axis.

The general (or standard) form of a linear

equation is denoted by ax by c, where a, b,

and c are real numbers, a and b cannot both be

0. These are examples of linear equations

4x 2y 6.2 y 3.7x 5 y 3 These are

not linear equations x2 y2

9

Find the x-and-y-intercepts of the linear

equation 3x ¾ y 18. To find the

x-intercept, set y 0 and solve for x. 3x ¾

(0) 18 3x 18 x

6 or the ordered pair (6, 0) To find the

y-intercept, set x 0 and solve for y. 3(0) ¾

y 18 ¾ y 18 (4/3)(¾) y

18(4/3) y 24 or the ordered

pair (0, 24)

Graphing a Line Method 1 Using a table of

values Create a table of values, plot the

ordered pairs, and connect the points with a

straight line.

Graph the equation 2x y 6 by using a table

of values. Pick a set of x-values, substitute

them (one at a time) into the equation to find

the corresponding y-value. x 1

2(1) y 6 2 y 6

2 2 y 6 2

y 4 Plug this value into the table and

repeat this process for x 0 and x 2. Plot the

ordered pairs, and connect the points with a

straight line.

x y

-1

0

2

x y

-1 4

0 6

2 10

Graphing a Line Method 2 Using the

intercepts Find the x-intercept, find the

y-intercept, plot the intercepts, and connect the

points with a straight line.

Use the intercepts to graph 3x 4y

24. x-intercept 3x 4(0) 24 3x 24 x 8

x-intercept is (8, 0) y-intercept 3(0)

4y 24 4y 24 y 6 y-intercept

is (0, 6) Now plot the intercepts, and connect

the points with a straight line.

Maria needs to purchase graphing calculators and

engineering paper for her students. She has 3225

in her budget. The calculators cost 129 each,

and the packages of engineering paper cost 15

each. The equation 129x 15y 3225 represents

Maria's purchases. Find and interpret both

intercepts. x-intercept 129x 15(0)

3225 x 25 Maria can buy 25 calculators

and no engineering paper for 3225. y-intercept

129(0) 15y 3225 y 215 Maria

can buy 215 packages of engineering papers and no

calculators for 3225.

Special Note

- The x-intercept is also known as the horizontal

intercept. - The y-intercept is also known as the vertical

intercept.

- Interpreting Horizontal and Vertical Intercepts
- from a Graph
- To help you interpret the intercepts, first

determine - what is represented by the horizontal axis and

the - vertical axis.

After a tropical storm, Jerrys air boat was

flooded with 40 gallons of water and he had to

remove the water with his onboard sump pump. The

graph below depicts the amount of water G (in

gallons), left in the boat after t minutes of

using the sump pump. Use the graph to find and

interpret both intercepts in the context of the

problem. The horizontal axis, t,

represents Time in minutes The vertical axis, G,

represents Gallons of Water The horizontal

intercept is (25, 0). The sump pump will remove

the water from the boat after 25 minutes. The

vertical intercept is (0, 40). Before the sump

pump was used, there were 40 gallons of water in

the boat.

- Writing equations from

application problems - Luigi has 84 to spend in apps for his iPad. He

wants to buy action - and sports games apps. The action games he likes

cost 10.50 - each and the sports games cost 7 each. Let x

represent number - of action games apps and y represent number of

sport games apps. - a. Write an equation that describes what Luigi

can purchase with - his money.
- Action games at 10.50 each Sports games at 7

each 84 - 10.50x 7y 84
- b. If Luigi only purchases action games apps, how

many can - he buy?
- Since no sports games apps are bought, then y

0. - 10.50x 7(0) 84
- x 8

- (Contd.)
- c. If Luigi only purchases sports games apps, how

many can - he buy?
- Our equation was 10.50x 7y 84
- Since no action games apps are bought, then x

0. - 10.50(0) 7y 84
- y 12 Luigi can buy 12 sports games

apps. - d. Sketch the graph of the linear equation using

your answers - from parts (b) and (c).
- Using the x-intercept, (8, 0), and the

y-intercept, (0, 12), we can - graph the linear equation

- Viewing Window Notation for Graphing

Calculator - Xmin, Xmax, Xscl by

Ymin,Ymax,Yscl - Given that a line has intercepts (30, 0) and (0,

125), which of the - following viewing windows will be the most

appropriate? - a. 35, 10, 5 by 30, 120, 20
- b. 50, 40, 10 by 40, 140, 20
- We are looking for a viewing window that will

show both intercepts. - Only b will display both (30, 0) and (0, 125).

- Option a will not show the y-intercept, since

the Y-max is 120.

Using your textbook, practice the problems

assigned by your instructor to review the

concepts from Section 1.1.