GRAPHING EQUATIONS. 6.EE.9 Use variables to represent two quantities in a real- world problem that change in relationship to one another; write an equation.

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Presentation transcript:

GRAPHING EQUATIONS

6.EE.9 Use variables to represent two quantities in a real- world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable Objective: Understand how to graph an equation on the Cartesian Coordinate Plane Learning target: Answer at least 3 out of 4 coordinate plane questions on the exit ticket.

*If you replace the variables with the x and y coordinates of the point you get a true equation. y = x = ? 5 = 5 *What does it mean if a point satisfies an equation? Prove that (3, 5) satisfies y = x + 2

(1, 4)? 4 = 3(1) + 1? 4 = 3 + 1? 4 = 4 (3, 0)? 0 = 3(3) + 1? 0 = 9 + 1? 0 = 10 X (0, 1)? 1 = 3(0) + 1? 1 = 0 + 1? 1 = 1 Which points satisfy y = 3x + 1? (1, 4) (3, 0) (0, 1)

*Plot every single point that solves the equation. For our previous example of y = 3x + 1, we saw that (1, 4) and (0, 1) are solutions, so those points will be plotted. There are other points that work also. But how do we figure out these points? It would take too long to test every single point and hope that our equation works. *How do you graph an equation?

x is the independent variable. You pick a number for x. Independent means it is not controlled. You get to pick whatever number you want for x. y is the dependent variable. Substitute x into the equation to calculate y. Dependent means it relies on something else. You do not get to pick y, you have to calculate it. This gives you one point (x, y). Repeat with a different x until you have enough points. How do we find points to graph?

Pick x = 1: y = 2(1) + 1 y = 3 Plot (1, 3) Pick x = 2: y = 2(2) + 1 y = 5 Plot (2, 5) Pick x = 0: y = 2(0) + 1 y = 1 Plot (0, 1) Graph y = 2x + 1 You could have picked any number for x. x = 1000: y = 2(1000) + 1 y = 2001 But now you have to plot (1000, 2001) on your graph. Choose reasonable numbers.

Your answers will be different depending on what numbers you chose for x. Here are some sample points: (-3, -1), (-2, 0), (-1, 1), (0, 2), (1, 3), (2, 4), (3, 5) Find three points for y = x + 2

Graph: y = x²