1.1 Tables and Graphs of Linear Equations

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Presentation transcript:

1.1 Tables and Graphs of Linear Equations Objectives: Represent a real-world linear relationship in a table, graph, or equation. Identify linear equations and linear relationships between variables in a table. Standard: 2.8.11 Q Represent functional relationships in tables, charts, and graphs.

A (2, 4) B (-3, 5) C (0, 1) D (-2, 0) E (4, -5) F (-2, -1) I. Plot the following ordered pairs on a coordinate graph. Label the four quadrants. * A (2, 4) B (-3, 5) C (0, 1) D (-2, 0) E (4, -5) F (-2, -1)

II. How do you know whether an equation is linear? There needs to be a constant difference between consecutive x-values and a constant difference between consecutive y-values. Can always be written in slope intercept form y =mx + b. The variable X can never be raised to a power i.e. y = x2 There cannot be a variable in the denominator.

II. State whether each equation is linear. y = -3x YES y = ½ x-3 YES y = x2 + 1 NO y = 1/x NO y = 5 – 4x YES y = -4/x NO

III. Graph a linear equation III. Graph a linear equation. y = mx + b, m is the slope and b is the y intercept (0, b).* plot the y-intercept, (0, b). beginning at the y-intercept use the slope (rise/run) to find a second point. y = 3x + 2 y = 2x b = (0,2) m = 3 b = (0,0) m = 2

III. Graph a linear equation III. Graph a linear equation. y = mx + b, m is the slope and b is the y intercept (0, b).* 2y = 4x + 8 y + 4 = x - 3 y = x - 7 y = 2x + 4 m = 2 b = (0, 4) m = 1 b = (0, -7)

IV. Determine whether each table represents a linear relationship between x and y. If the relationship is linear, write the next ordered pair that would appear in the table. (5, -5) X Y 1 3 2 -1 4 -3 Y = -2x + 5

IV. Determine whether each table represents a linear relationship between x and y. If the relationship is linear, write the next ordered pair that would appear in the table. X Y -4 -7 -2 -1 2 4 5 6 8 (8, 11) Y = 3/2x - 1

V. Word Problems Ex. 1 An attorney charges a fixed fee of $250 for an initial meeting and $150 per hour for all hours worked after that. A. Make a table of the total charge for 1, 2, 3, and 4 hours worked.

C. Write a linear equation to model this situation. B. Graph the points represented by your table and connect them. C. Write a linear equation to model this situation. .

D. Find the charge for 25 hours of work.

Ex. 2 A water tank already contains 55 gallons of water when Dan begins to fill it. Water flows into the tank at a rate of 9 gallons per minute. A. Make a table for the volume of water in the tank after 1, 2, 3, and 4 minutes. V. Word Problems time x 1 2 3 4 gallons y 64 73 82 91

Graph the points represented by your table and connect them.* V = 9T + 55 Volume (V) Time (T) D. Find the volume of water in the tank 20 minutes after Dan begins filling the tank. V = 9 (20) + 55 V = 235

Integrated Algebra II- Section 1.1 Level A Homework Integrated Algebra II- Section 1.1 Level A Academic Algebra II- Section 1.1 Level B