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SWBATUnderstand the meaning of the word slope
Find the slope using two points on a line
Determine the difference between positive slope, negative slope, zero slope
Show lines that have the same slope are parallel
Understanding SlopeSlope is the ratio of the vertical change to
the horziontal change
In other words: Slope is the steepness of a line
Mathematical Facts about Slope
Slope is denoted by the letter m
The vertical change (change in y) is called the rise
The horizontal change (change in x) is called the run
Find the Slope by Graphing:Find the slope of a line that goes through points (- 3, 5)
and (2,1)Plot the points
Now SolveWe counted DOWN 4 spots, so we moved (– 4) units
We counted RIGHT 5 spots, so we moved 5 units
So our slope is:
m = - 4/5
Using Math to Find Slope
When given two points (x1, y1) and (x2, y2) you can find the slope of a line by using the following formula:
GroupTry: Without graphing Find the Slope of a line through
points (2,1) and (4,4)
Remember:
Hint: Identify (x1, y1) and (x2, y2)
Try on your ownFind the slope through the points (7, -4) and (9, 4)
Find the slope through the points (9, - 2) and (3, -5)
Answer: m = 4
Answer: m = - ½
Slope and Steepness
The greater the number, the steeper the slope (“faster” it moves up or down)
The smaller the number, the more gentle the slope (“slower” it moves up or down)
m = 4 >> m =1/4 >>
Classifying SlopePositive Slope – Slants up from left to right (“uphill”)
Negative Slope – Slants down from left to right (“downhill”)
Classifying SlopeZero Slope – Line is horizontal (driving an a flat road)
Undefined Slope – Line is vertical (straight up and down) – Can you drive a car up a wall? NO!
In Your Group1) What is the slope of the line
represented by the table of values below?
Answer: m = 10
x y
0 - 20
1 - 10
2 0
3 10
Which statement best describes the slope of the line
graphed above?The slope is – 6
The slope is 2/3
The slope is 3/2
The slope is – 4
If you said: The slope is 2/3
You were WRONG!
The slope is 3/2
Ticket to LeaveWrite the slope formula using m, x1, y1, x2, y2
Find the slope of the line that passes through the points (-2, 5) and (4, -5)
Describe the difference between the graph of a line with a positive slope and a negative slope
Describe the difference between the graph of a line with zero slope and undefined slope