Graphing Linear Equations and Inequalities

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1 Algebra I Name: Date: Period: # Graphing Linear Equations and Inequalities Linear Equation/Inequalities equations/inequalities that will be represented using lines on the coordinate plane. Assignments (1) 1.7 and 3.7 Page #10 24 Even; Page 177 #15, 18, 26 (2) 4.8 Page #12, 16, 18, all (3) 4.4 Page 230 #12 35 LEFT (4) 4.4 Page #22 34 RIGHT and #38, 40 and 42 Quiz Tomorrow (5) Page #14, 16, 18, 32, 35, (Graph Paper Needed) (6) Page , 23, 26, 32, 38, Page 222 #44, 47; Page #18, 27, 30, 33(Graph Paper Needed) (7) Page #18, 30, 36, 48, 51; Page #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 #15, 19, 23, 27, 35 #43 48 (Graph Paper Needed) (12) Page #18, 28, 36, Even (Graph Paper Needed) Quiz Tomorrow (13) Page #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 P a g e

2 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 Output Input Output The collection of all input values is the of the function and the collection of all output values is the of the function. E1. Does the table represent a function? Input Output 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 = x P a g e

3 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 = 1 h(b1 + b2) for b2 2 P4. Solving a Temperature Conversion Formula Solve the temperature formula C = 5 (F 32) for F. 9 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. 3 P a g e

4 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 1. Given a set of ordered pairs: Examine the domain (set of inputs) a. If the domain repeats, then the relation is not a function (Repeat/Relation) 2. Given a graph: Use the Vertical Line Test a. 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. a. b. E2. Decide whether the relation is a function. If it is a function, give the domain and range. a. Input Output b. Input Output P a g e

5 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. a. b. Input Output Input Output 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 a. f(x) = -2x 3 when x = -2 b. g(x) = x 2 when x = -3 P4. Evaluate the function for the given value of the variable a. f(x) = -2x + 1 when x = 1 b. g(x) = 2x 2 3 when x = -2 5 P a g e

6 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 = rise change in y = = y 2 y 1 run change in x x 2 x 1 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) 6 P a g e

7 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) 7 P a g e

8 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. a. (2, 3) b. (-1, 2) y = 1 2 x + 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) 8 P a g e

9 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. 9 P a g e

10 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. a. Rewrite in slope-intercept form b. Plot the y-intercept (b) c. Follow the slope (m) Graphing Equations of Lines Applications (E) 10 P a g e

11 E1. An Internet Service Provider estimates that the number of households h (in millions) with Internet access can be modeled by h = 6.76t , where t represents the number of years since Graph this model. Describe the graph in context of the real life situation Internet Access Households (millions) t h 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: Adults: x Students: y Verbal Model: Equation: Zoo Fundraising Possible Prices to Raise $1500 Student Adult (x) (y) P a g e

12 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. a. What is your rate of change in height? Use the formula for slope to find the rate of change. Verbal Model Rate of Change = Change in height Change in time b. About when will you reach the ground? Verbal Model Time = Distance Rate 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 = 1 t t 60 2 Stage 2 (next 12 hours): h = 54 60<t 72 Stage 3 (last 48 hours): h = - 5 t <t Flood Stages of River P a g e

13 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 < c ax +by c ax + by > c ax + 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: 1. Graph the corresponding equation a. < and > - use dashed line b. and - use solid line 2. Test a point 3. 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 a. (0, 0) b. (0,1) c. (2, -1) E2. Graph: x < P a g e

14 6.5 Graphing Linear Inequalities in Two Variables (I,E) E3. Graph: y 1 E4. Graph: x + y > 3 P1. Graph: 2x + y < 1 14 P a g e

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Writing Linear Equations and Inequalities

Algebra Name: Date: Period: # Writing Linear Equations and Inequalities Linear Equation/Inequalities equations/inequalities that will be represented using lines on the coordinate plane. (1) Write each