1. Algebra 1 – 3.10 and 3.11 Equations and graphs

2. x + y = 5 Fill in the table so that the points satisfy the equation. Graph the (x, y) coordinates that satisfy the equation. What shape is the graph? XY(x, y) 14(1, 4) 2 -3 0 1/2 -2 -11/3

3. 2x + 3y = 12 Find 5 points that satisfy the equation. Find 5 points that do not.

4. y – x 2 = -1 (y – 3) = -1(x – 2) y = |x| Sketch a graph of the (x, y) coordinates that satisfy the equation. What shape is the graph?

5. y = x 2 – 3x + 2 The graph: What values of x make y=0?

6. 3.11 – Equations as Point- Testers

7. To graph an equation Some (x, y) pairs will make the equation true. We plot those. Some (x, y) pairs will make the equation false. We do not plot them. If you plot ALL the (x, y) pairs that make the equation true, the result is a graph of the equation.

8. How will you know if a point is part of an equations graph? Equation: 2x + 3y = 12 Will these points be on the graph? (6, 0) (10, 2) (4, 1)

9. Plot the points that work 2x + 3y = 12 xy2x + 3y =12?

10. POINT-TESTER When graphing, use the equation as a point-tester If a point passes the test, it goes on the graph. If a point fails the test, it does not

11. GRAPH of an equation Definition: the collection of all points with coordinates that make the equation true

12. Example: y = -1

13. A habit of mind… representing solutions Equations can have none, one, or many solutions In this chapter, we will look for points (pairs of numbers) that satisfy equations with two variables There are INFINITE solutions Two ways to represent -list of points (hard to do infinite…) -graph

14. Ex: y=4 Name and plot six points on its graph Describe the graph. Sketch in the rest of the graph. If you get a point (a, b), how will you know whether or not the point is on the graph?

15. Ex: x 2 + y 2 = 25 Are these points on the graph? (5, 0) (-3, 0) (-3, 4) Find 4 more points on the circle.

16. Ex: y = x Find 5 points on the graph. Find 5 points not on the graph. What does the graph of the equation look like? Draw the graph and explain why it correctly represents the equation.

17. Absolute Value… |x|=3 |3|=x |x|=-3 |x-1|=3