2 Learning Goal #1 for Focus 4 (HS.A-CED.A.2, HS.REI.ID.10 & 12, HS.F-IF.B.6, HS.F-IF.C.7, HS.F-LE.A.2): The student will understand that linear relationships can be described using multiple representations.4321In addition to level 3.0 and above and beyond what was taught in class, the student may:· Make connection with other concepts in math· Make connection with other content areas.The student will understand that linear relationships can be described using multiple representations.- Represent and solve equations and inequalities graphically.- Write equations in slope-intercept form, point-slope form, and standard form.- Graph linear equations and inequalities in two variables.- Find x- and y-intercepts.The student will be able to:- Calculate slope.- Determine if a point is a solution to an equation.- Graph an equation using a table and slope-intercept form.With help from theteacher, the student haspartial success with calculating slope, writing an equation in slope-intercept form, and graphing an equation.Even with help, the student has no success understanding the concept of a linear relationships.
3 Standard or General Form: Ax + By = CWhere A, B and C are numbersx and y are the variablesA and B are called coefficients
4 3 Rules for Standard Form Get the variables on the left and the constant on the right!You must have the leading coefficient as a positive integerYou must have all numbers A, B and C as integers (whole numbers)
5 How to change from slope-intercept form to Standard form Step 1: Clear out any fractions or decimals by multiplying all numbers by the denominator or by the place value of the decimal.Step 2: Move the x and y variable to the left side. Keep the constant on the right side.Step 3: Make sure the x coefficient is positive. If not, multiply all terms by -1.
6 Practice: y = ¾ x + 2 (4)y = (4)¾ x + (4)2 Get rid of fractions. -3x -3x Move all variables to the left.-3x + 4y = 8 Make first coefficent positive.(-1)(-3x) + (-1)(4)y = (-1)(8)3x – 4y = -8
7 What about decimals? y = -0.24x - 5.2 Multiply through by 100 to clear decimals, then put in standard form.(100)y = (100)(-0.24) – (100)(5.2)100y = -24x – 52024x + 100y = (Now reduce if possible.)24x + 100y =6x + 25y = -130
8 Real-life example:You have $6.00 to use to buy apples and bananas. If bananas cost $.49 per pound, and apples cost $.34 per pound, write an equation that represents the different amounts of each fruit you can buy. Graph it.Let x = bananas and y = apples
9 .49x + .34y = 6Since we are using standard form, we will multiply through by 100 to clear out decimals.Therefore: 49x + 34y = 600What do we do now to graph this?
10 Find the x and y intercepts. x-intercept (12, 0) and y-intercept (0, 18)The graph will be in the first quadrant only.ApplesBananas
11 Practice:Put in standard form the line passing through point (2, -3) with a slope of 3.3x – y = 9Put in standard for the horizontal line going through point (-2, 6)y = 6