1. The Slope of a Line with Ed and Leslie

2. (2, 1) (8, 9) Hey Ed, How many lines can go through two points? That is easy Les,1 Right That line looks awfully steep. Let’s figure out its slope. We always have so much fun together. The slope is the change in the vertical distance divided by the change in the horizontal distance. That sounds like an equation. Of course there is an equation, it’s math class isn’t it? I can hardly wait to figure out the slope. This is so exciting. Your wait is over. Wow, that is amazing. Should we review? We better. 6 8

3. To Find the Slope of a Line 1.Select any two points on the line 2.Find the vertical change by subtracting the y-coordinates, in any order 3.Find the horizontal change by subtracting the x-coordinates, in the same order as the y-coordinates 4.Write the ratio of the vertical change to the horizontal change Hey, Ed let’s do some examples That’s a great idea

4. Slope Examples (-3, -2) (4, 7) Hey Ed, go out on the grid Okay Les My turn Let’s find the slope Great Let’s change Okay (-6, 7) (4, 2) Should we find the slope? Of course Hey, when the line points in this direction the slope is negative! Good observation! How about if we look at some other examples? I can’t wait

5. Slope Examples (2, 3) (11, 3) I wish I had a notebook, I would write that down. Hey Les, We are lined up. Hey Les, horizontal lines have a slope of 0 Let’s change again. I see Ed. Let’s look at the slope. That is right Ed. I don’t know about this. (5, 1) (5, 9) Let’s see what happens. Vertical lines have undefined slope That’s right Ed, time for another review.

6. The Slope of a Line 1.Positive Slope: 1.As x increases, y increases, slants upward 2.Negative Slope: 1.As x increases, y decreases, slants downward 3.Zero Slope: 1.Horizontal lines have zero slope 4.Undefined Slope: 1.Vertical lines have undefined slope Hey, Ed let’s look at a point and a slope That sounds like fun.

7. It’s not so hard: the slope is the change in y over the change in x. Point and Slope Example (2, 4) Through the point (2,4) draw the line whose slope is -⅔ What ??? A slope of -⅔ is equal to -2 over 3. So y decreases by 2 and x increases by 3 I get it! The next point will be (2+3,4 +(-2)) or (5,2) Correct (5, 2) 3 2 I need a review. Okay

8. The Slope of a Line 1.The slope of a line is the change in the vertical distance over the change in the horizontal distance. 2.The slope of a line is constant, that is, it is the same between any two points on the line. 3.To find the slope of a line: a.Select any two points on the line b.Find the vertical change by subtracting the y-coordinates, in any order c.Find the horizontal change by subtracting the x-coordinates, in the same order as the y-coordinates d.Write the ratio of the vertical change to the horizontal change

9. The Slope of a Line 1.Types of Slope ⁄Positive Slope:  As x increases, y increases, slants upward \Negative Slope:  As x increases, y decreases, slants downward — Zero Slope:  Horizontal lines have zero slope │Undefined Slope:  Vertical lines have undefined slope 2.Given a point (a,b) and a slope, find another point on the line by:  Adding the numerator of the slope to the y-coordinate: b+n  Adding the denominator of the slope to the x-coordinate: a+m  The new point is (a+m, b+n)

10. Mathematical HistoryMathematical History 1.The slope of a line is often denoted by the variable “m”. 2.Using the letter m for slope is attributed to the mathematician René Descartes (1596-1650). 3.The grid we work with is called the Cartesian Plane 4.The letter m is derived from the French verb monter – to climb/to rise That was interesting. You know what happens now? What? It’s practice time. Yay!