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SLOPE INTERCEPT FORM OF A LINEAR FUNCTION WARM-UP (TAKS 2006) OBJECTIVES TSW investigate, describe and predict the effects of b, the y-intercept, in the linear equation. TSW identify the slope and y-intercept in a linear equation. Key Concept The slope intercept form of a linear equation is written as y = mx + b slope y-intercept SLOPES Positive Zero Negative Undefined SLOPE Ratioof the vertical change (the rise) to the horizontal change (the run) between any two points on the line. Slope: rise m run FORMULA TO FIND THE SLOPE OF A LINE y2 y1 m x2 x1 GRAPH THE FUNCTIONS Y = 2X, Y = 3X AND COMPARE WITH Y = X. (M > 0) y = 2x m>0 The bigger y=x the slope, the steeper y=½x the graph of the line. The smaller the slope, less steep is y = 3x the line. GRAPH THE FUNCTION Y = -2X, Y = -3X AND COMPARE WITH Y = X AND Y = -X y = -2x m<0 y=x The bigger the slope, the steeper the graph of the line. y = -½ x y = -3x y = -x Y-INTERCEPT (math) to cut off or mark off between two points, lines, etc. (Webster’s New World Dictionary, 2003) y-intercept: the y-coordinate of a point where a graph crosses the y-axis. Means that x = 0 GRAPH THE FUNCTION F(X) = X + 4 AND COMPARE WITH F(X) = X f(x) = x + 4 The graphs have f(x) = x the same slope, but different y-intercepts. Graphs of this family are vertical translations of the graph of f(x) = x. GRAPH THE FUNCTION F(X) = X – 5 AND COMPARE WITH F(X) = X f(x) = x The graphs have the same slope, f(x) = x – 5but different y-intercepts. Graphs of this family are vertical translations of the graph of f(x) = x. GRAPH THE FUNCTION F(X) = -X + 3 AND COMPARE WITH F(X) = -X The graphs have the same slope, but different y-intercepts. f(x) = -x + 3 f(x) = -x Graphs of this family are vertical translations of the graph of f(x) = x. CHOOSE THE GRAPH THAT BEST MATCHES THE FOLLOWING EQUATIONS y = 2x + 2 B _____ y = 2x – 8 D _____ y = 2x + 6 _____ A y = 2x – 3 C _____ A B C D IDENTIFY THE SLOPE AND Y-INTERCEPT OF THE FOLLOWING EQUATIONS y = 3x + 5 y = -3x m=3 m = -3 b=5 b=0 y = -x – 6 2y = 8x – 6 m = -1 m=4 b = -6 b = -3 2x – 8 = y 4y = 4x – 1 m=2 m=1 b = -8 b = -¼ IDENTIFY THE SLOPE AND Y-INTERCEPT OF THE FOLLOWING EQUATIONS 2y – 3x = 5 2x + 4y = -8 m = 3/2 m = -½ b = 5/2 b = -2 WRITE AN EQUATION GIVEN THE FOLLOWING INFORMATION m=7 m = -2 b = -2 b = -7 y = 7x – 2 y = -2x – 7 b = -9 m=½ m = -3 b=-¾ y = -3x – 9 Y = ½x – ¾ WRITE AN EQUATION IN SLOPE-INTERCEPT FORM OF THE LINE SHOWN 10 9 Slope 8 7 m=2 6 5 y-intercept 4 3 b = -2 2 1 Equation 0 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 y = 2x – 2 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 WRITE AN EQUATION IN SLOPE-INTERCEPT FORM OF THE LINE SHOWN 10 9 Slope 8 7 m = -3/2 6 5 y-intercept 4 3 b = -1 2 1 Equation 0 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 y = -3/2x – 1 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 WRITE AN EQUATION IN SLOPE-INTERCEPT FORM OF THE LINE SHOWN 10 9 Slope 8 7 m=½ 6 5 y-intercept 4 3 b=3 2 1 Equation 0 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 y = ½x + 3 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 PRACTICE WORKSHEET

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posted: | 8/6/2012 |

language: | English |

pages: | 21 |

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