Objective The student will be able to find
Objective The student will be able to: find the slope of a line given 2 points and a graph. SOL: A. 6 a Designed by Skip Tyler, Varina HS and Vicki Hiner, Godwin HS
What is the meaning of this sign? 1. 2. 3. 4. Icy Road Ahead Steep Road Ahead Curvy Road Ahead Trucks Entering Highway Ahead
So, what is slope? ? ? Slope is the steepness of a line.
Slope is represented by the variable: m m = Rise Run Rise: how much a line goes up or down Run: how much a line moves left to right
m = 2 2 Rise Run Rise= 2 Run= 2 Rise m = Run = So, the Slope, m = 1 2 2
We read graphs as we read a book. From LEFT to RIGHT
There are four different kinds of slope (m). . .
And 2 Special Cases… The zero-fun coaster The impossibly scary coaster What kind of slope are they?
Aw! That’s zero fun!
That’s a really scary coaster, so the slope is…
For the following slides, raise your hand when you know if the slope is positive, negative, zero, or undefined.
ne gat ive
ti ve si po
zero
undefined
Example 1) Determine the slope of the line. . . When given the graph, it is easier to apply rise run
Determine the slope of the line. Start with the lower point and count how much you rise and run to get to the other point! 6 3 rise 3 = = run 6 Notice the slope is positive AND the line increases!
Finding the Slope of a line Slope (m) has a formula: m= Rise change in y = Run change in x
Find the slope of the line that passes through the points (-2, -2) and (4, 1). When given points, it is easier to use the formula! y 2 is the y coordinate of the 2 nd ordered pair (y 2 = 1) y 1 is the y coordinate of the 1 st ordered pair (y 1 = -2)
Slope Formula x 1 y 1 x 2 y 2 Given (5, -3) and (-4, 2), find the slope of the line. m= You match the coordinates with the x’s and y’s. *Be Consistent*
Find the slope of the line that passes through (3, 5) and (-1, 4). 1. 2. 3. 4. 4 -4 ¼ -¼
Find the slope of the line that goes through the points (-5, 3) and (2, 1).
Determine the slope of the line shown. 1. 2. 3. 4. -2 -½ ½ 2
Determine the slope of the line. 1 -2 Find points on the graph. Use two of them and apply rise over run. The line is decreasing (slope is negative).
What is the slope of a horizontal line? The line doesn’t rise! All horizontal lines have a slope of 0.
What is the slope of a vertical line? The line doesn’t run! All vertical lines have an undefined slope.
Draw a line through the point (2, 0) that has a slope of 3. 1 3 1. Graph the ordered pair (2, 0). 2. From (2, 0), apply rise over run (write 3 as a fraction). 3. Plot a point at this location. 4. Draw a straight line through the points.
e g n e l l a h C
The slope of a line that goes through the points (r, 6) and (4, 2) is 4. Find r. To solve this, plug the given information into the formula
To solve for r, simplify and write as a proportion. Cross multiply. 1(-4) = 4(4 – r)
Simplify and solve the equation. 1(-4) = 4(4 – r) -4 = 16 – 4 r -16 -20 = -4 r -4 -4 5=r The ordered pairs are (5, 6) and (4, 2)
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