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Math 9 Unit 4: Linear Relations Section 4.3: Another form of the equation of a linear relation Terminology Parallel Lines: Lines that run in the same direction and never touch. Perpendicular Lines: Lines that cross each other at a 90° angle. Vertical Line: a line that extends up and down. Runs parallel to the y-axis and perpendicular to the x-axis. Horizontal Line: a line that extends left and right. Runs parallel to the x-axis and perpendicular to the y-axis. Oblique Line: a line that is drawn at an angle. Runs neither parallel nor perpendicular to either axis on a graph. Graphing and Describing Horizontal and Vertical Lines (Text Page 178 #4, 5, 6, 7, 8, 12) The graph of the equation x = a , where a is a constant, is a vertical line that passes through the a on the x-axis. Every point on the graph has an x-coordinate of a. The graph of the equation y = a , where a is a constant, is a horizontal line that passes through the a on the y-axis. Every point on the graph has an y-coordinate of a. 1 Math 9 Unit 4: Linear Relations 1. For each equation i. Graph the equation ii. Describe the graph a. x = -4 b. y+2=0 c. 2x = 5 2. Does each of the following describe a vertical line, horizontal line, or an oblique line? a. x = -5 b. y – 2 = 0 c. 3x + y – 12 = 0 2 Math 9 Unit 4: Linear Relations 3. Write an equation and describe the line in the graph provided. a. b. y y 1 - 10 10 -5 5 x 10 5 -1 -2 -1 1 2 3 x -3 -5 -4 -5 - 10 4. Which equation best describes the graph given? a. b. x–3=0 3x + 6 = 0 c. d. 3y – 6 = 0 3x – 6 = 0 y 10 5 -4 -3 -2 -1 1 2 x -5 - 10 3 Math 9 Unit 4: Linear Relations Graphing an equation in the form ax + by = c (Text Page 178 #10, 11, 14, 15, 17, 21) When given an equation that does not have y by itself, we can rearrange the equation first so that it is in slope-intercept form. 1. Rearrange each of the following equations to slope-intercept form. a. b. c. x + y = 5 4x + 3y = 12 -2x – 2y = 6 d. 1x–1y=1 4 2 e. 1x+1y=6 2 3 f. -2.5x + 0.5y = 7 2. For the equation 3x – 2y = 6 a. Make a table of values for -4, 0, 4. b. Graph the equation. 4 Math 9 Unit 4: Linear Relations 3. The difference of two numbers is 8. Let x represent the greater number and y represent the lesser number. a. Complete a table for 8 different values of x. b. Graph the data. Should you join the points? c. Write an equation that relates x and y. 5