1. HA1-385: Finding the Slope of a Line

2. What is SLOPE?
Slope, in math, describes the STEEPNESS of a line. How is slope used in LIFE????
Skiers LOVE good slope. The steeper the slope, the faster you go!!

3. What is SLOPE? Slope is STEEPNESS of a line.
Amusement park engineers use slope to design rides.

4. What is SLOPE? Slope is STEEPNESS of a line.
Home builders & architects use it to design homes. A roof has slope.

5. What is SLOPE? Slope is STEEPNESS of a line.
Road builders use slope to design roads that rain will run off.

6. How do we use slope in Algebra class?
We look at lines to learn about steepness
( slope) so we can apply our knowledge later.
When you graph a line, you need x’s and y’s.
A lot of equations we use have two variables, an x and a y.
These equations represent lines we can graph.

7. How do we use slope in Algebra class?
Equations can look like y=3x+5 , which could represent the situation
“you pay $5 to get into the arcade, and then $3 for every game you play” ,
- It can be graphed to represent ALL of the different combinations of # of games played .

8. How do we use slope in Algebra class?
Equations that look like y=3x+5 can be graphed.
We will learn how to graph these equations in a future lesson.

9. How do we use slope in Algebra class?
Equations can look like -3x + y=5 .
We will how to transform these equations into a “y=mx + b” equation called slope intercept form.
This is the EASIEST equation to graph from and will be your FRIEND.
Let’s Learn!

10. m = m = (y2−y1) (x2−x1) rise run What we will learn in THIS lesson
1. To find the slope from TWO points
like ( 2,3) and (1,4) using
2. To find slope from a graph using
(y2−y1)
m =
(x2−x1)
M is the variable letter used to represent SLOPE
rise
m =
run

11. The slope (m) of a line describes its steepness.
It is determined by its:
a) vertical change (or rise)
b) horizontal change (or run)

12. A line that moves upward from left to right has a positive slope.
I’m positive this uphill is
hard work
A line that moves downward from left to right has a negative slope.
WEE….this downhill is easy, don’t be so negative.

13. Two lines that have the same slope are parallel.
Horizontal lines have a slope of 0.
Vertical lines have an undefined slope.

14. The slope (m) of a line is measured by the vertical change in y or (rise) over the horizontal change in x or (run).
m =
change in y
change in x or
rise
m =
rise
run
run

15. You can find the slope (m) of a line by using the rise and the run of the line.1 4
8 ft.
The slope of the ramp is 1/4.

16. You can find the slope (m) of a line by using the coordinates of any 2 points on the line to find the change in y and the change in x. y x
(y2−y1)
or rise
(x2, y2)
m =
(x2−x1)
or run
(x1, y1)

17. m = m = y2 − y1 x2 − x1 (2) − (−1) + m = 3 4 ( 2) − (−2) +
Find the slope (m) of a line passing through the following points by finding the change in y and the change in x.
(x1,y1) (x2,y2)
A (-2,-1), B (2,2)
m =
y2 − y1
x2 − x1
(2) − (−1) +
( 1)
m = 3 4
m =
( 2) − (−2) +
( 2)
The slope of the line is 3/4 .

18. m = m = m = y2 − y1 x2 − x1 (−2,-2) & (3,0) 0 − (−2) 2 2 5 3 − (−2) 2
Find the slope (m) of a line passing through the following points by finding the change in y and the change in x.
(x1, y1) (x2,y2)
m =
y2 − y1
x2 − x1
(−2,-2) & (3,0)
0 − (−2) + 2
m = 2 5
m =
3 − (−2) + 2
The slope of the line is 2/5 .

19. m = m = m = y2 − y1 x2 − x1 (-3,3) & (3,−2) −2 − 3 −5 6 3 − (−3) 3
Find the slope (m) of a line passing through the following points by finding the change in y and the change in x.
(x1, y1) (x2, y2)
m =
y2 − y1
x2 − x1
(-3,3) & (3,−2)
−2 − 3 3
m =
m = −5 6
3 − (−3) 3 +
The slope of the line is − 5/6 .

20. Zero Slope m = = = x y y2 − y1 3 − 3 x2 − x1 5 − 2 3
ZERO Slope, like the worst ski slope ever!
OR graphed
OR from two given points ( 2, 3) and ( 5, 3) =
Where’s the hill??
Zero slope graphed. y x
Zero slope
Zero slope
m =
y2 − y1
x2 − x1
3 − 3
5 − 2 3 = =

21. No Slope or Undefined Slope
I am heading into undefined territory!! Yahoo!!
No or Undefined Slope is like a CLIFF!
Same as undefined slope
No slope graphed.
No SLOPE from two given points, (-4, 3) and (-4, -2)
Undefined slope.
So STEEP, it has NO SLOPE!!
m =
y2 − y1
x2 − x1
-2 − 3
-4 − -4 -5 = = = No
Slope

22. m = m = rise run x The slope of the line is 3/4 . y
Find the slope (m) of this line by finding the rise and the run of the line:
m =
rise
run y x
(2, 2) 3
m = 4
(−2, −1)
The slope of the line is 3/4 .

23. m = m = rise run x The slope of the line is − 5/6 . y
Find the slope (m) of this line by finding the rise and the run of the line:
m =
rise
run
(−3, 3) y x −5
m = 6
The slope of the line is − 5/6 .
(3, −2)

24. Take a Look………….. Think about this!
The next two slides aren’t in THIS lesson, but you will have to do them very soon……
Take
a Look…………..

25. Graph the line that contains the point (−2,−2) and has a slope of
m =
2 rise
3 run
A second point on the line is (1, 0). Use the two points to graph the line.
(1, 0)
(−2,−2)

26. Graph the line that contains the point (−3,2) and has a slope of .
m =
−3 rise
5 run
(−3,2)
A second point on the line is (2,− 1). Use the two points to graph the line.
(2, −1)