8-3 Horizontal and Vertical Lines 8-3 Horizontal and Vertical Lines
8-3 Horizontal and Vertical Lines 8-3 Horizontal and Vertical Lines
8-3 Horizontal and Vertical Lines 8-3 Horizontal and Vertical Lines
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Mrs. Aitken’s Integrated 1 MathUnit 8 Linear Equations as Models8-3 <strong>Horizontal</strong> <strong>and</strong> <strong>Vertical</strong> <strong>Lines</strong>Warm-upSolve each equation.1. 2x = 136 x = 682. d + 5 = 39 d = 343. 117 – n = 91 n = 264. 4 + 3n = 19 n = 55. 67 = 25 + k k = 428-3 <strong>Horizontal</strong> <strong>and</strong> <strong>Vertical</strong> <strong>Lines</strong>rise y2 − y1Slope = = run x − x2 1Facts about horizontal <strong>and</strong> vertical linesType of line Slope Equation Function?<strong>Horizontal</strong> 0 y = a Yes<strong>Vertical</strong> No slope, undefined x = b NoExample 1Sketch the line through the points (2, -2) <strong>and</strong> (5, -2). Then write an equationfor the line.Solution 1Plot the two points <strong>and</strong> draw a line passing through them.(2, -2) (5, -2)8-3 <strong>Horizontal</strong> <strong>and</strong> <strong>Vertical</strong> <strong>Lines</strong>
Mrs. Aitken’s Integrated 1 MathUnit 8 Linear Equations as Modelsrise change in y −2 −( −2) 0slope = = = = = 0run change in x 2 −5 −3The slope is zero. The y-coordinate of all the points on this line is –2.The equation of the line is y = -2.Example 2Graph the equation 4x – 24 = 0 on the coordinate plane.Solution 2Most linear equations have two variables in them. When a linear equation has only onevariable, you know that the line is either horizontal or vertical, depending on the variableinvolved.Solve for x4x− 24=0+ 24 + 244x= 244x24=4 4x = 6To graph this line, plot several points (x, y) where the value of x is 6.(6, 0), (6, 1), (6, 2), (6, 6)8-3 <strong>Horizontal</strong> <strong>and</strong> <strong>Vertical</strong> <strong>Lines</strong>
Mrs. Aitken’s Integrated 1 MathUnit 8 Linear Equations as ModelsThe line is vertical.rise change in y 3−1 2slope = = = = = undefinedrun change in x 6 − 6 0Since division by zero is undefined, the slope is undefinedExample 3Find the slope of the line <strong>and</strong> write an equation for the line.(-6, -7.6) (9, -7.6)Solution 3The slope is 0. The equation is y = -7.6Example 4Find the slope of the line <strong>and</strong> write an equation for the line.(1.2, 4)(1.2, -2)Solution 4The slope is undefined.The equation is x = 1.28-3 <strong>Horizontal</strong> <strong>and</strong> <strong>Vertical</strong> <strong>Lines</strong>
Mrs. Aitken’s Integrated 1 MathUnit 8 Linear Equations as ModelsExample 5Write an equation for each line.a. The points (9, 3) <strong>and</strong> (-1, 3) are on the line.b. The slope is undefined, <strong>and</strong> the point (-1, 4) is on the line.Solution 5a. slope = (3-3)/(9-1) = 0/8=0 <strong>Horizontal</strong> liney = 3b. x = -1 <strong>Vertical</strong> lineExample 6On the same set of axes, graph the equations x = 3 <strong>and</strong> y = 2. Where do thelines intersect?Solution 6The lines intersect at the point (3, 2).Summary<strong>Vertical</strong> lines have an undefined slope.<strong>Horizontal</strong> lines have a slope of zero.ReviewWrite in slope-intercept form1. 5x + 9y = 452. 0x – 11y = 22Solve3. –2(x + 4) = 84. 3t + 7 = 5 – 2t8-3 <strong>Horizontal</strong> <strong>and</strong> <strong>Vertical</strong> <strong>Lines</strong>
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