Graphing Linear Equations and Inequalities

Algebra IName:

Date:

Period:

Linear Equation/Inequalities – equations/inequalities that will be represented using lines on the coordinate plane.

Assignments

(1)1.7 and 3.7 Page 49 – 50 #10 – 24 Even; Page 177 #15, 18, 26

(2)4.8 Page 259 – 260 #12, 16, 18, 20 – 28 all

(3)4.4 Page 230 #12 – 35 LEFT

(4)4.4 Page 230 – 231 #22 – 34 RIGHT and #38, 40 and 42 Quiz Tomorrow

(5)Page 214 – 215 #14, 16, 18, 32, 35, 41 – 45 (Graph Paper Needed)

(6)Page 221 17, 23, 26, 32, 38, Page 222 #44, 47; Page 244 – 245 #18, 27, 30, 33(Graph Paper Needed)

(7)Page 221 – 222 #18, 30, 36, 48, 51; Page 244 – 245 #36, 42, 45 and 46 (Graph Paper Needed) Quiz Tomorrow

(8)4.2 Applications Page 216 #67 - 73

(9)4.3 Applications Page 222 #60 – 66, Page 232 #56 - 60

(10)4.4 Applications Page 245 #56 – 58, 60 and 61

(11)Page 363 – 364 #15, 19, 23, 27, 35 #43 – 48 (Graph Paper Needed)

(12)Page 363 – 364 #18, 28, 36, 50 – 58 Even (Graph Paper Needed) Quiz Tomorrow

(13)Page 264 – 266 #6 – 16 Even, 22, 24, 30 and 32

(14)Chapter Review Test for *******TEST TOMORROW*******

(15)Standardized Test Prep Page 59 #17, 18, Page 268 #1 – 9 Page 388 #8 and 9

1.7 Introduction to Functions (I,E)

A ______is a rule that establishes a relationship between two quantities, called the ______and the ______.

**For each input there is exactly one output**

Input / 0 / 1 / 3 / 4
Output / 3 / 1 / 1 / 2

The collection of all input values is the ______of the function and the collection of all output values is the ______of the function.

Input / Output
1 / 3
2 / 6
3 / 11
4 / 18

E1. Does the table represent a function?

E2. Make an input-output table for the function. Use 0, 1, 2 and 3 as the domain.

y = 3x + 2

E3. Make an input-output table for the function. Use 1, 1.5, 3, 4.5 and 6 as the domain.

y = x2 – 0.5

3.7 Formulas and Functions (I, E)

A ______is an algebraic equation that relates two or more real-life quantities.

E4. Solving Area of a Trapezoid

Solve the area of a trapezoid formula A = h(b1 + b2) for b2

P4. Solving a Temperature Conversion Formula

Solve the temperature formula C = (F – 32) for F.

E5. Rewrite the equation 1 + 7y = 5x – 2 so that y is a function of x.

P5. Rewrite the equation 3x + y = 4 so that y is a function of x.

4.8 Functions and Relations (I,E)

A ______is defined to be any set of ordered pairs.

A function is a relation in which each input corresponds to exactly one output.

Two ways to determine if a relation is a function

Given a set of ordered pairs: Examine the domain (set of inputs)
If the domain repeats, then the relation is not a function (Repeat/Relation)
Given a graph: Use the Vertical Line Test
If any vertical line can be drawn to pass through two or more points on the graph, then the graph is not a function (Repeat/Relation)

E1. Decide whether the graph represents y as a function of x. Explain your reasoning.

E2. Decide whether the relation is a function. If it is a function, give the domain and range.

4.8 Functions and Relations (I,E)

E3. Decide whether the relation is a function. If it is a function, give the domain and range.

Input / Output
1 / 2
2 / 4
3 / 4
4 / 5

Input / Output
1 / 5
1 / 7
2 / 7
3 / 9

Function Notation

f(x) is read “f of x” and is a way to represent functions. f(x) simply takes the place of y.

E4. Evaluate the function for the given value of the variable

f(x) = -2x – 3 when x = -2b. g(x) = x2 when x = -3

P4. Evaluate the function for the given value of the variable

a. f(x) = -2x + 1 when x = 1b. g(x) = when x = -2

4.4 Slope of a Line (E)

The ______m of a nonvertical line is the number of units the line rises or falls for each unit of horizontal change from left to right. (aka steepness of a line)

Given two points (x1, y1) and (x2, y2):

Slope = = =

Positive slope means line rises from left to right

Negative slope means line falls from left to right

Zero slope means line is horizontal (HOY)

Undefined slope means line is vertical (VUX)

E1. Plot the points and draw a line through them. Without calculating, state whether the slope of the line is positive, negative, zero or undefined. Explain.

(7, 4) and (-1, 8)

E2. Plot the points and find the slope of the line passing through the points.

(1, 5) and (5, 2)

4.4 Slope of a Line (E)

E3. Plot the points and find the slope of the line passing through the points.

(7, 4) and (7, 8)

E4. Plot the points and find the slope of the line passing through the points.

(-1, 5) and (3, 5)

P1. Plot the points and find the slope of the line passing through the points

(2, 7) and (3, 1)

4.2 Graphing Linear Equations-Equation, Table and Graph (E)

E1. Use the graph to decide whether the point lies on the graph of the line. Justify your answer algebraically.

(2, 3)
(-1, 2)

E2. Decide whether the given ordered pair is a solution of the equation.

6y – 3x = -9; (2, -1)

E3. Rewrite the equation in function form

2x + 3y = 6

Graph using a table of values. Label each graph on the coordinate plane.

E4. y + 2 = 3x

E5. -3x = 6 (VUX)

E6.2y + 1 = 9 (HOY)

4.3 Quick Graphs Using Intercepts (E)

An ______is the x – coordinate of a point where the graph crosses the x-axis. A ______is the y-coordinate of a point where the graph crosses the y-axis.

E7. Find the x-intercept and the y-intercept of the graph of the equation 2x + 3y = 6

E8. Graph the equation y = 4x + 4 using the intercept method.

4.6 Quick Graphs Using Slope – Intercept Form (E)

Slope – Intercept Form (SIF)

y = mx + b

The ______of the line is m

The ______of the line is b

E9. State the slope and y-intercept of the graph of y = -x + 2

E10. Write the equation in slope-intercept form (SIF).

2x – 4y = 16

E11. Graph the equation 3x + y = 2 using the slope-intercept method.

Rewrite in slope-intercept form

Plot the y-intercept (b)

Follow the slope (m)

Graphing Equations of Lines Applications (E)

E1. An Internet Service Provider estimates that the number of households h (in millions) with Internet access can be modeled by h = 6.76t + 14.9, where t represents the number of years since 1996. Graph this model. Describe the graph in context of the real life situation.

t / h
0
1
2
3
4
5
6

E2. Zoo Fundraising: You are organizing the annual spaghetti dinner to raise funds for the zoo. Your goal is to sell $1500 worth of tickets. Assuming 200 adults and 100 students will attend the dinner, how much should you charge for an adult ticket and for a student ticket?

Key:Verbal Model:

Adults: x

Possible Prices to Raise $1500
Adult (x) / Student (y)

Students: yEquation:

Graphing Equations of Lines Applications (E)

A ______of ______compares two different quantities that are changing. Slope provides an important way of visualizing a rate of change.

E3. You are parachuting. At time t = 0 seconds, you open your parachute at height h = 2500 feet above the ground. At time t = 35 seconds, you are at height h = 2115 feet.

What is your rate of change in height?

Use the formula for slope to find the rate of change.

Verbal ModelRate of Change =

About when will you reach the ground?

Verbal ModelTime=

E4. City Planning: You are an intern at a city planner’s office and are asked to create a graph for a planning board meeting. The graph will represent different heights of a local river during a flood.

You are given the following equations to model the changing river heights. In each equation, h represents the height of the river (in feet) and t represents the time (in hours) since the flooding began.

Stage 1 (first 60 hours): h = t + 24 0≤t≤60 Stage 2 (next 12 hours): h = 54 60<t≤72

Stage 3 (last 48 hours): h = -t + 99 72<t≤120

6.5 Graphing Linear Inequalities in Two Variables (I,E)

A ______in x and y is an inequality that can be written as follows.

ax +by < cax +by ≤ cax + by > cax + by ≥ c

An ordered pair (x,y) is a ______of a linear inequality if the inequality is true when the values of x and y are substituted into the inequality.

Steps:

Graph the corresponding equation
< and > - use dashed line
≤ and ≥ - use solid line
Test a point
If the test point is a solution, shade the half-plane it is in. If not, shade the other half plane

E1.Check whether the ordered pair is a solution of 2x – 3y ≥ -2

(0, 0)b. (0,1)c. (2, -1)

E2. Graph:x < -2

6.5 Graphing Linear Inequalities in Two Variables (I,E)

E3.Graph:y ≤ 1

E4.Graph:x + y > 3

P1. Graph:2x + y < 1

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