Formulas for Linear FunctionsWhat Do You Know about These Forms of Linear Equations?Slope and Y-InterceptSlide 4Slide 5SlopeGraphing a FunctionCreating a Function from a TableSlide 9Slide 10Finding Formulas from Verbal DescriptionUsing a Graph to Find a FormulaAssignmentFormulas for Linear FunctionsLesson 1.42What Do You Know about These Forms of Linear Equations?0( )1Ax By Cy mx by k m x hx ya b+ + == +- = -+ =Standard formStandard formSlope Intercept formSlope Intercept formSlope-Point form(h,k) a point on the linem = the slopeSlope-Point form(h,k) a point on the linem = the slopeTwo Intercept formTwo Intercept form3Slope and Y-Intercept•Consider y = m * x + b•The m and b are called parametersthey affect the appearance of the graph•The m is the slopem > 0 line is up to the rightm < 0 line is down to the rightm = 0 horizontal line|m| large very steep line4Slope and Y-Intercept•Considering y = m * x + b•The b is the y-interceptWhere on the y-axis, the line intersects•On your calculatorGo to Y= screenEnter at Y1 (2/3) * x + 5Predict what the graph will look like before you specify F2, 6 for standard zoom5Slope and Y-Intercept•The function y = (2/3) * x + 5•Slope = 2/3 (up to the right)•Y-intercept = 5 •6Slope •When slope = •Try y = -7x – 3(predict the results before you graph)2 change in y3 change in xyxD= =D3xD =2yD =7Graphing a Function•y = -7x – 3•Do the slope and y-intercept agree with your prediction?7 771 1yxD -=- = =D -7 771 1yxD -=- = =D -y-intercept = -3y-intercept = -38Creating a Function from a Table•Determine slope by usingx y3 74 8.55 106 11.5change in ychange in xymxD= =DxDyD10 7 35 3 231.52yxymxD = - =D = - =D= = =DAnswer:9Creating a Function from a Table•Now we know slope m = 3/2•Use this and one ofthe points to determiney-intercept, b•Substitute an orderedpair into y = (3/2)x + bx y3 74 8.55 106 11.5310 5220 3 5 25 252bbbb= �+= �+==3 5:2 2solution y x= +10Creating a Function from a Table•Double check results•Substitute a different ordered pair into the formulaShould give a true statement3 5:2 2solution y x= +x y3 74 8.55 106 11.511Finding Formulas from Verbal Description•Read exercise 40, pg 34 of text•Profit y = ___ x + ______where x is number of patrons?•What does the slope mean?•What does the y-intercept mean?•How many patrons are needed to start making money?•How could you represent patrons p = ____ x + _____where x is the amount of profit?12Using a Graph to Find a Formula•Given a graphwith two points•Use the points todetermine slope, m•Substitute (x,y) from one of points tofind b•Answer:••(2,7)(8, 3.4)0.6 8.2y x=- +13Assignment•Lesson 1.4•Page 32•Exercises1 – 9, 11, 13, 15, 17, 19, 21, 23, 29, 37,
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