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Transcript
Math 10 Linear Functions Review y mx b is the general equation of a linear function m = slope ex. y x y y1 m= 2 x2 x1 m= m= The slope of the line that passes through (2,1) and (-3,0) y x m= y 2 y1 x2 x1 m= ◊ Horizontal Lines have a slope of zero! 4 0 1 32 m= Ex. y 3 y 3 2 1 x –4 –3 –2 –1 1 2 3 4 –1 –2 –3 –4 ◊ Vertical Lines have an undefined slope 4 Ex. x 2 y 3 2 1 x –4 –3 –2 –1 1 –1 –2 –3 –4 2 3 4 1 5 m= 1 5 ◊ Parallel Lines have equal slopes 4 y 3 2 1 x –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 –1 –2 –3 –4 ◊ Perpendicular Lines have negative reciprocal slopes 4 y 3 2 1 x –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 –1 –2 –3 –4 ◊ Positive slopes have graphs that rise to the right 4 y 3 2 1 x –7 –6 –5 –4 –3 –2 –1 1 –1 –2 –3 –4 2 3 4 5 6 7 7 ◊ Negative slopes have graphs that decrease to the right 4 y 3 2 1 x –6 –4 –2 2 4 6 –1 –2 –3 –4 From y = mx + b, “b” is the y-intercept (0, b) ex. For y = -3x + 1 4 y 3 b = 1, so the y-intercept is (0,1) 2 1 x –6 –4 –2 2 4 6 –1 –2 y-intercept (0,1) –3 –4 Finding the intercepts (where the graph crosses the x and y axes) x-intercept (let y = 0) y-intercept (let x = 0) ex. What is the x-intercept of the linear function y 3x 2 ? 0 = 3x - 2 2 = 3x 3 3 2/3 = x x-int. (2/3, 0) ex. What is the y-intercept of the linear function y 2x 1? Y = 2(0) + 1 Y=0+1 Y=1 y-int. (0, 1) Point-Slope Equation is useful y y1 m( x x1 ) Ex. Find the equation of a line that has a slope of 2 and passes through (1, 3) y 3 2( x 1) Graphing using the Intercept method (x, 0) and (0, y) Given an equation not in the General Form, the intercept method is a useful way of graphing (without having to rearrange the equation) Ex. Graph -4x + 1 = 2y -3 The x-intercept can be found when y = 0. -4x + 1 = 2(0) – 3 -4x + 1 = -3 -4x = -3-1 -4x = -4 4 4 x=1 The y-intercept can be found when x = 0. -4(0) + 1 = 2y – 3 1 = 2y – 3 1 + 3 = 2y 4 = 2y 2 2 2=y x-intercept is (1, 0) y-intercept is (0, 2) 4 y 3 2 1 x –6 –4 –2 2 –1 –2 –3 –4 4 6 Finding and Equation given… (a) (b) (c) (d) (e) (f) two points slope and one point slope and the y-intercept (a point) slope and the x-intercept (a point) Parallel or Perpendicular to another line and a point The graph (visually) Note - Remember that you know how to move variables and numbers from one side of the equation to the other. You can solve for y if the equation is not in the general equation of y=mx+b