1

Graphing Linear Equations and Functions

2

3

Today’s Date: ____________

4.1 Plot Points in a Coordinate Plane

Quadrant: _______________________________________________________________

Give the coordinates of the point.

A: _____________

B: _____________

C: _____________

D: _____________

E: _____________

E

D

C

BA

4

Plot the point in a coordinate plane.

Describe the location of the point.

1. _________ 2. _________ 3. _________

Location: ______________ Location: ______________ Location: ______________

Graph the function. Then identify the range of the function.

4. 5.

x y = x + 1 y

-2 y = -2 + 1 -1

-1

0

1

2

Range: ___________________ Range: ___________________

x 3x2

1y +−= y

-4

-2

0

2

4

5

Performing Transformations (pg. 213-214)

For a given set of points, a __________________________ produces an image by applying a rule to the coordinates of the points. Some types of transformations are translations, vertical stretches, vertical shrinks, and reflections.

A _______________________ moves every point in a figure the same distance in the same direction either horizontally, vertically, or both.

Perform a translation

The transformation (x, y) � (x, y + 3) moves ∆ABC up ______________.

Original Image

A (1, 0) A’ (1, 3) B (2, 2) B’

C (3, 0) C’

A vertical ____________ or ______________ moves every point in a figure away from the x-axis (a vertical stretch) or toward the x-axis (a vertical shrink), while points on the y-axis remain fixed.

The transformation (x, y) � (x, 2y) vertically

_____________ ∆ABC Original Image

A (1, 0) A’ (1, 0)

B (2, 2) B’

C (3, 0) C’

6

A ____________ flips a figure in a line.

The transformation (x, y) � (x, -y)

____________ ∆ABC Original Image

A (1, 0) A’ (1, 0)

B (2, 2) B’

C (3, 0) C’

For additional practice problems check out page 214 in your algebra book!

7

Today’s Date: ____________

4.2 Graph Linear Equations

Linear Equation: ___________________________________________________________

Standard Form of a linear equation: ____________________________________________

Linear Function: ___________________________________________________________ _______________________________________________________________________

Graph an equation:

A. _____________________ B. _____________________

8

Graph y = b and x = a.

C. _____________________ D. _____________________

E. y = 2x - 1 F. x = -3

G. y = -4x + 1 H. y = -3

Equations of Horizontal and Vertical Lines:

1. The graph of y = b is a ________________ line.

2. The line of a graph y = b passes through the point ___________.

3. The graph of x = a is a ________________ line.

4. The line of a graph x = a passes through the point ___________.

9

Graph the function with domain x ≥ 0. Then identify the range of the function.

I. y = 2x + 2 J. y = -x + 4

K. L.

10

11

Today’s Date: ____________

4.3 Graph Using Intercepts x-intercept: ______________________________________________________________

y- intercept: _____________________________________________________________

Find the x-intercept and the y-intercept of the graph of 8x – 2y = 16.

1. Substitute ____ for y and solve for x.

2. Substitute ____ for x and solve for y.

3. Graph the x and y intercepts and connect the points.

12

Find the x-intercept and y-intercept of the graph of the equation.

A. 2x + 3y = 18 B. -12x – 4y = 36

Use a graph to find the intercepts.

Identify the x-intercept and y- intercept of the graph.

C. D.

E. Graph 2x – 7y = 14. Label the points where the line crosses the axes.

13

Today’s Date: ____________

4.4 Find Slope and Rate of Change

Slope: __________________________________________________________________

Rate of Change: ___________________________________________________________

Find the Slope of a Line.

Find a Slope.

14

Find the slope of the line passing through the points.

A. (-3, -1) and (-2, 1) B. (-6, 3) and (5,-2)

Find the Slope of a Line

C. D.

Find the slope of the line passing through the points. Then classify the line by its slope.

E. (1, -2) and (1, 3) F. (-3, 7) and (4, 7)

15

Find a rate of change.

timeinchange

tcosinchangechangeofRate =

Gas Prices: The table shows the cost of a gallon of gas for a number of days. Find the rate of

change with respect to time.

Time (days) Day 1 Day 2 Day 3

Price/ gal ($) 1.99 2.09 2.19

The table shows the change in temperature over time. Find the rate of change in ° Fahrenheit

with respect to time.

Temperature (°F) Time (hours)

38 0

43 2

48 4

53 6

16

17

Today’s Date: ____________

4.5 Graph Using Slope-Intercept Form

Slope-intercept form: ______________________________________________________

Parallel: ________________________________________________________________

Finding the Slope and Y-Intercept of a Line

18

Identify the slope and y-intercept.

A. y = x + 3 B. -2x + y = 5

C. y = 4x – 1 D. 4x – 2y = 8

E. 4y = 3x + 16 F. 6x + 3y = -21

Graph an Equation Using Slope-Intercept Form.

4x + y = 2

1. Rewrite the equation in slope-intercept form.

2. Identify the slope and y-intercept.

3. Plot the point that corresponds to the y-intercept.

4. Use the slope to locate a second point on the line.

5. Draw a line through the two points.

19

Graph an Equation Using Slope-Intercept Form.

1yx2

1 =+−

m = ________ b = ________

Identify Parallel Lines.

Find the slope of each line.

Line a:

Line b:

Line c:

Line a

Line c

Line b

20

Determine which lines are parallel. Line a: through (2, 5) and (-2, 2)

Line b: through (4, 1) and (-3, -4)

Line c: through (2, 3) and (-2, 0)

21

Today’s Date: ____________

4.6 Model Direct Variation

Direct Variation: _________________________________________________________ _______________________________________________________________________

Constant of Variation: ______________________________________________________ _______________________________________________________________________

Identify direct variation equations.

Tell whether the equation represents direct variation. If so, identify the constant of

variation.

A. 3x + 4y = 0 B. 5x + y = 1

22

Graph direct variation equations.

C. y = -5x D. x5

3y=

Write and use a direct variation equation.

1. Write the direct variation equation. 2. Find the value of y when x = 80.

23

Today’s Date: ____________

4.7 Graph Linear Functions Function notation: _________________________________________________________ _______________________________________________________________________

Family of functions: ________________________________________________________ _______________________________________________________________________

Parent linear function: ______________________________________________________ _______________________________________________________________________

Find an x- value.

A. For the function f(x) = 3x + 1, find the value of x so that f(x) = 10.

B. For f(x) = 6x – 6, find the value of x so that f(x) = 24.

C. For f(x) = 7x + 3, find the value of x so that f(x) = 17.

24

Graph a function.

Text Messages

A wireless communication provider estimates that the number of text messages m (in millions) sent over several years can be modeled by the function m = 120t + 95 where t represents the

number of years since 2002. Graph the function and identify its domain and range.

t M

0

1

2

3

Use the model from above to find the value of t so that m = 1055. Explain what the solution means in this situation.

Parent Function for Linear Functions

1. The ___________________________________ is the most basic linear function.

2. __________________ is the form of the parent linear function.

25

Compare graphs with the graph f(x) = x

Graph the function. Compare the graph with the graph of f(x) = x.

A. p(x) = x – 4 B. q(x) = -2x

C. x2

1)x(r =

26

Compare Graphs of Linear Functions with the Graph of f(x) = x

g(x) = x + b The graphs have the _________ slope.

The graphs have different_____________. Graphs of this family are

________________________________ of the graph f(x) = x.

g(x) = mx where m > 0 The graphs have different (positive)

________.

The graphs have the same_____________.

Graphs of this family are vertical

__________ or ___________ of the graph f(x) = x.

g(x) = mx where m < 0 The graphs have different (negative)

________.

The graphs have the same_____________.

Graphs of this family are vertical __________ or ___________ or

______________ of the graph f(x) = x.