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GraphingGoals: 1. (Df = Q)2. Graph a line given its equation using either:

i. Table of values.ii. Slope/intercept method.

3. Graph horizontal and vertical lines.

Notation:

(Df = Q)

Graphing lines

5h3Using a table of values to graph a line given the equation:

* in the last examples, you choose the x coordinates! (because every x has a y, choosing a useful pattern of x coordinates will lead to a pattern of y coordinates!)

a.

y = x +2

b.

y = 2x -1

c. d. e

x y x y x y x y x y0 -21 -12 03 14 2

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Using the slope and y-intercept to graph the line:

Step 1: plot the y-intercept (this is the (0|t) in y = mx + t or the (0, b) in y = mx +b )

Step 2: from the y-intercept, count the slope m = then plot the next point. Repeat and join.

(Or: first lightly sketch the directly proportional line with the same slope and then move the entire line up and draw it so that it crosses at the correct y-intercept. Erase the first sketch.)

Ex. Graph the line given the equation using the y-intercept/slope method:

a.

b.

c. f(x) = -5x

d.

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Horizontal and vertical lines:

Fill in the table of values for the following.

a. y = 3 b. x = -2

x xy y

What do you notice?

Graph the points. What do you notice?

Practice:Graph:a. y = -3b. y= 5c. y= 10

d. x = 2e. x= -1/2f. x= -8

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Practice Questions:

Complete the table of values for each of the following equations and graph the line.

19

20

22

23

24

x y x y x y x y x y-3 0 -1 -2 7

0 0 1 0 -71 2 1 -4 0

25

28

29

30

31

x y x y x y x y x y0 2 0 1 -15 0 -3 -2 310 -1 5 4 -3

Graph the lines by creating a table of values with at least 3 sets of points.

34. x = y +2 35. y= x - 4 36. -3x + y = -6 37. 2x – 5y = 10

38. y = 4x 39. y = -2x 40. 42.

Indicate if each of the following statements is true or false. If it is false, rewrite it to be true.

67. The line x = 3 is horizontal. 68. The line y = -4 is horizontal.

69. A line parallel to the y-axis 70. A line perpendicular to the x-axis is vertical. is vertical.

75. Graph each linear function, f, (Df = Q) ( lines using the slope and y-intercept method. (Zeichne jeweils ein Koordinatensystem und trage dann den Graphen der linearen Funktion f (Df = Q) mithilfe seiner Steigugn und seines y-Achsenabschnitts ein.

a. b. c. d.

e. f. g. h.

i. j. k. l.

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m. n. o. p.

Welche der Geraden mit positiver (negativer) Steigung verläuft am steilsen? Find Paare von Geraden, die zueinander parallel sind.

Answers for odd questions:

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Answers: 75.

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