3.1 Notes - A linear equation can be put in standard form...

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3.1 Graphing Equations Equation in 2 variables: y=4x+4 Solution consists of two numbers that make the equation true: an x value and a y value. Solution is written as an ordered pair (x,y) Is (1,8) a solution? Is (2,5) a solution? Sub 1 for x and 8 for y: sub 2 for x and 5 for y: Y=4x+4 8=4(1)+4 5=4(2)+4 8=8 True! 5=12 Not true! So (1,8) is a solution So (2,5) is not a solution To find more solutions, pick an x value and solve for y x y -1 0 0 4 1 8 2 12 3 16 4 20 An equation in two variables has an infinite number of solutions! We can graph an equation in two variables to visualize all solutions. To graph y=4x+4, make a table of ordered pair solutions, then plot the points: 35 30 25 20 15 10 5 5 10 15 20 25 40 30 20 10 10 20 30 40 50 60 Every point on the line is a solution of y=4x+4 Use the graph to predict what y will be when x=5 or x=-3
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The equation we just graphed is an example of a linear equation in two variables, because its graph is a line. How can you tell if an equation is linear? It is linear if there are no absolute values or exponents on x or y in the equation.
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Unformatted text preview: A linear equation can be put in standard form: Ax + By = C (A and B are not both 0) To put an equation in standard form, get all variables on the left side of the equation and the constant term on the right side. y = 4x + 4-4x -4x-4x + y = 4 or 4x – y = -4 x-intercept : point where a graph crosses the x-axis y-intercept : point where a graph crosses the y-axis To find x-intercept, let y=0 and solve for x To find y-intercept, let x=0 and solve for y To graph any linear function: A) Find a least two ordered pair solutions (I prefer three) B) Plot the ordered pairs C) Draw a line through them Example: ½ x – y = 0 First solve for y: y = ½ x Make a table of solutions: x y-2-1 2 1 8 6 4 2 2 4 6 8 10 5 5 10 15 To graph non-linear equations, we need to find more ordered pair solutions. Example: y = x² x y-3 9-2 4-1 1 1 1 2 4 3 9 Example: y = |x| x y-3 3-2 2-1 1 1 1 2 2 3 3 You can also graph equations on a graphing calculator!...
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