1. Graphing Review Get a piece of graph paper and fold it so you have 4 graph positions on the front (fold once hamburger, once hot dog, then unfold) Make sure you have a straight edge, too.

2. Graph using HoffmaSlope… ( 0, -4 ) Point Slope 3 Slope is a DIRECTION…it points to the next point on a line! For HoffmaSlope to work, we need the Slope in the form of a fraction +U –D R Start at the given point… Then SAY the fraction… +U 3 OVER 1 That is our direction to the next point. Up 3 Over 1 Up 3Over 1

3. Graph using HoffmaSlope… ( -3, 0 ) Point Slope Slope is a DIRECTION…it points to the next point on a line! For HoffmaSlope to work, we need the Slope in the form of a fraction +U –D R Start at the given point… Then SAY the fraction… –D 1 OVER 4 That is our direction to the next point. Down 1 Over 4 Down 1 Over 4

4. Now…GRAPH IT slope-intercept style! Remember… Slope is m y - int is b Down 3 Over 1 Down 3 Over 1 y – int means where the line TOUCHES the y-axis That’s the starting point! Slope…

5. Graph this… We could work the formula to put it into slope-intercept form… But there is a different way… HoffmaMagic! Find the intercepts! If a point is on the y -axis, what is the value of x ? If a point is on the x -axis, what is the value of y ? NOTE: graph counts by 2s

6. Chapter 9 Unit Question – How do we solve linear systems?

7. Section 1 Essential Question How do we solve a linear system by graphing?

8. What is a system? a set of sentences joined by the word “and” which together describe a single situation

9. Verify that this solution is true: (6, -4) In other words, does (6, -4) work in both equations? 2x + y = 8 x – y = 10 2(6) + (-4) = 8 12 – 4 = 8 8 = 8 YES!! 6 – (-4) = 10 6 + 4 = 10 10 = 10 YES!!! Solution to a system is called … THE INTERSECTION!

10. Graph both and find the INTERSECTION!!! y = 2x - 2y = ½x - 2 Intersection is ( 0, –2 )

11. Graph both and find the INTERSECTION!!! x + y = 5y = -3x +3 Intersection is ( –1, 6 )

12. Graph both and find the INTERSECTION!!! y = xx = 2 Intersection is ( 2, 2 )

13. Graph both and find the INTERSECTION!!! y = 2x + 1y = 2x 2 + 1 Intersections are ( 0, 1 ) AND ( 1, 3 )

14. Graph both and find the INTERSECTION!!! HUH?!?!? y = x + 4y = x - 3 Intersection is – THERE IS NONE

15. The sum of two numbers is 3 The difference is -1 Translate both statements into equations… x + y = 3 x – y = -1 GRAPH and find the solution to both (INTERSECTION!) Intersection is ( 1, 2 )

16. Homework Do HoffmaSheet 9 – 1