1. Writing linear equations given two points 5.3 12/5/13

2. The slope of a line… Mathematicians have developed a useful measure of the steepness of a line, called the slope of the line. Slope compares the vertical change (the rise) to the horizontal change (the run) when moving from one fixed point to another along the line. A ratio comparing the change in y (the rise) with the change in x (the run) is used calculate the slope of a line.

3. The Slope of a Line Definition of Slope The slope of the line through the distinct points (x 1, y 1 ) and (x 2, y 2 ) is where x 1 – x 2 = 0. Definition of Slope The slope of the line through the distinct points (x 1, y 1 ) and (x 2, y 2 ) is where x 1 – x 2 = 0. Change in y Change in x = Rise Run = y 2 – y 1 x 2 – x 1 (x 1, y 1 ) x1x1 y1y1 x2x2 y2y2 (x 2, y 2 ) Rise y 2 – y 1 Run x 2 – x 1 x y

4. The Possibilities for a Line’s Slope Positive Slope x y m > 0 Line rises from left to right. Zero Slope x y m = 0 Line is horizontal. m is undefined Undefined Slope x y Line is vertical. Negative Slope x y m < 0 Line falls from left to right.

5. Finding Slope… We can find slope 2 ways 1 - Graphing 2 - Slope equations

6. Finding Slope... Find the slope of the line through the points (4, 1) and (-1, 5)

7. Finding Slope... Find the slope of the line through the points (0, -1) and (5, 9)

8. Finding Slope.. Find the slope of the line through the points (3, 4) and (3, 9)

9. Sample Problems: Find the slope of the line thru the points given:  (-3,-1) and (-2,4)  (-3,4) and (2,-2)

10. So…Writing Equations Now… When Given 2 points, first find the slope. Once you find the slope, you have a slope and a point (2 points actually!) Plug in the slope and a point to find the equation

11. Hold up… If we have two points, does it matter which one we choose? No…Since both points are on the line, doesn’t matter which one we choose.

12. Writing Equations Find the equation of the line passing through the points: (0, -1) and (5, 9)

13. Writing Equations Find the equation of the line passing through the points: (1, 6) and (3, -4)

14. Writing Equations Find the equation of the line passing through the points: (6, -3) and (0, 9)

15. Writing Equations Find the equation of the line passing through the points: (4, -6) and (4, 4)

16. Homework: On your handout…  Place your name, date, and hour on the worksheet  Write all answers and show all work!!!  Worksheet due Tuesday, 12/10/13