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2.2 Linear Equation Identify linear equations and functions. Write Linear equations in standard form Definition of a Linear equation No variable with an exponent other then 1. The only operation are addition, subtract and multiplication of a variable and a number. 4x + 3y = 15 or y = ½x or 7x = 9a - 24 Linear function A function whose ordered pairs satisfy a linear equation. Can be written as y = mx + b, where m is the slope or f(x) = mx + b Standard form Ax + By = C A, B and C are not fractions A and B are not both zero A is always Positive 6x – 3y = 18 Any y = mx + b can be written in Standard form y = -2x + 12 2x + y = 12 y = 4x – 14 -4x + y = - 14 4x – y = 14 add 2x to both sides subtract 4x to both sides then multiply both sides by – 1 What about y = ⅔x + 2 Multiply both sides by 3 to get rid of the fraction. 3y = 2x + 6 subtract 2x from both sides -2x + 3y = 6 Multiply by – 1 2x – 3y = - 6 No fractions, x and y are on the same side, A > 0. What is Standard form good for? Finding the X or Y intercept is easier to find with Standard form. Find the x intercept of 4x + 5y = 20 If a point is on the x axis, then what is its y value? What is Standard form good for? Finding the X or Y intercept is easier to find with Standard form. Find the x intercept of 4x + 5y = 20 If a point is on the x axis, then what is its y value? y=0 What is Standard form good for? Finding the X or Y intercept is easier to find with Standard form. Find the x intercept of 4x + 5y = 20 So 4x + 5(0) = 20 4x = 20 x=5 So the point would be (5,0) Finding the y intercept of 4x + 5y = 20 Last time we let y = 0, what shall we do this time. Finding the y intercept of 4x + 5y = 20 Last time we let y = 0, what shall we do this time. Let x = 0 4(0) + 5y = 20 5y = 20 y = 4 So the intercept is (0, 4) Is there another name for the y intercept? Lets graph an equation using the intercepts 6x – 2y = 18 x intercept 6x – 2(0) = 18 (3,0) x=3 Y intercept 6(0) – 2y = 18 (0, - 9) y = -9 Lets graph an equation using the intercepts 6x – 2y = 18 x intercept 6x – 2(0) = 18 x=3 Y intercept 6(0) – 2y = 18 y = -9 (0, - 9) 3 -9 (3,0) Homework Page 66 – 67 # 15 – 23 odd, 27 – 35 odd, 39 – 47 odd, 53 – 55, 64 – 76 even