1. First, Some Important slides from last time! Take Some Notes!
Slope and Stuff
First, Some Important slides from last time! Take Some Notes!

2. = Change in y = = Change in x =
Slope Intercept Form for a Line with a Slope of m and a y-intercept of b is…
Y-int.
Slope
Slope describes a lines its steepness, incline, decline or grade.
= Change in y =
= Change in x =

3. What the Slope? = Change in y = = Change in x =
Slope describes a lines its steepness, incline, decline or grade.
= Change in y =
= Change in x =

4. How do we calculate Slope With 2 Points?
If we have a point (x1, y1) and another point (x2, y2), how can we calculate slope?
Change in y (rise) over the Change in
x (run).
It looks likes this.
(x2, y2)
(x1, y1)

5. Example #1
If we have a point (x1, y1) and another point (x2, y2), how can we calculate slope?
(x2, y2)
(3, 3)
(x1, y1)
(0, 0) = m

6. Example #2
If we have a point (x1, y1) and another point (x2, y2), how can we calculate slope?
(x2, y2)
(3, 1) = = m
(1, -2)
(x1, y1)

7. Example #3
If we have a point (x1, y1) and another point (x2, y2), how can we calculate slope?
(x1, y1)
(-2, 1) = =
(x2, y2)
(2, -2) = m

8. Using Example #1 m = What is the y intercept? How do we find it?
Our equation is y = x + b (remember m = 1)
We have 2 Points! (3,3) and (0,0). Lets just plug one of them into our equation. Which is easiest?
(x2, y2)
(3, 3)
(x1, y1)
(0, 0)
y = x + b
0 = 0 + b
(0,0)
0 = b
So… y = x or… y = x!!

9. Find the y-int of example #2
Our two points = = m
(3, 1)
(1, -2)
(x2, y2)
Our equation
(3, 1)
What point to plug in?
(3, 1)
(1, -2)
(1, -2)
(x1, y1)

10. What is our equation for (3, 1) and (1,-2) then?= m
Yay!
Yay!
Yay!
Yay!
Yay!
Yay!
Yay!
Yay!
Yay!

11. Lets talk about the x-intercept!
So the y-intercept is where the line goes through the y axis, so the x-intercept is when
Our line goes through the x axis.
They go through points:
Our y-int.
(0,1)
Our x-int.
(-1,0)
Interesting… so
y is zero for the x-int!
Lets find the x-intercept for an equation!

12. Example #4 Find the x-intercept of: (x,0) y = x + 5 0 = x + 5 -x -x
Lets find the x-intercept for a harder equation!

13. Example #5 Find the x-intercept of: (x,0) y = -0.5x - 3 0 = -0.5x -3
/ /0.5
x = -6
Is our x-intercept!
(-6,0)

14. Vertical/Horizontal Line Discussion
What is the x-intercept of this vertical line?
It’s -3!!
So when y = 0, x = -3! What about when y = 2?
It’s also -3! It’s -3 everywhere!
So, x is not dependant on y, Therefore our equation of the line is x = -3

15. Vertical/Horizontal Line Discussion
What is the y-intercept of our vertical line?
Our equation of the line is x = -3
So, there will be no y-int
Sorry
y-int…

16. Vertical/Horizontal Line Discussion
What is the slope of our vertical line x = -3?
Let’s think about rise over run first.
Can’t divide be zero… Lets try 2 points, (-3,2) and (-3,0)
Can’t divide be zero

17. Vertical/Horizontal Line Discussion
What is the slope of our vertical line x = -3?
our slope is Undefined.
All vertical lines have an undefined slope.
Sorry
slope

18. Vertical/Horizontal Line Discussion
What is the x-int and y-int of a horizontal line?
y-int is 3. in fact, its 3 everywhere!
x-int does not exist.
So y = 3

19. Vertical/Horizontal Line Discussion
What is the slope of a horizontal line y = 3?
Let’s think about rise over run first.
Cool… Lets try 2 points, (1,3) and (2,3)

20. Vertical/Horizontal Line Discussion
What is the slope of our horizontal line y = 3?
our slope is 0.
All horizontal lines have a zero slope.