1. Slope and Rate of Change

2. Rates of change are seen everywhere.

3. The steepness of the roof of a house is referred to as the pitch of the roof by home builders.

4. Give one reason why some homes have roofs which have a greater pitch.
There is less snow buildup in the wintertime.

5. Engineers refer to the
rate of change of a road as the grade.

6. What is the meaning of this sign?
Icy Road Ahead
Steep Road Ahead
Curvy Road Ahead
Trucks Entering Highway Ahead

7. What does the 7% mean? 7% So, what is slope???
7% is the slope of the road. It means the road drops 7 feet vertically for every 100 feet horizontally.
7 feet
100 feet
So, what is slope???
Slope is the steepness of a line.
It is the rate it changes going up and down

8. SLOPE
Slope is the ratio of the vertical rise to the horizontal run between any two points on a line. Usually referred to as the rise over run.
Run is 6 because we went to the right
Slope triangle between two points. Notice that the slope triangle can be drawn two different ways.
Rise is 10 because we went up
Rise is -10 because we went down
Run is -6 because we went to the left
Another way to find slope

9. Slope is a measure of how much a line changes
Write this down—
Slope is a measure of how
much a line changes
going up and down ( or rise) for how much it changes
going left to right ( or run )

10. Linear functions have a constant rate of change
And this
Linear functions have a constant rate of change
Nonlinear functions do not

11. Types of Slope Complete Practice A Zero Negative Positive Undefined or
No Slope
Complete Practice A

12. If given 2 points on a line, you may find the slope using the formula
Write it on your paper

13. Find the slope of the line through the points (3,7) and (5, 19). x2 y2
m = 19 – 7
5 – 3
m = 12 2
m = 6
Complete Practice B

14. Find the missing coordinate if
the slope is 6
points (3, ) and (5, 19)
Solve by cross multiplying
Now try Practice C

15. Linear equations -only have 1 or 2 variables
-the variables are not multiplied together, - variables have a power of 1
Which of the following are linear?
Yes, they all are

16. Write this down.
3 common forms for linear equations
Slope intercept form y = mx + b
Point slope form
Standard form Ax + By = C
Today we are going start by talking
about slope intercept form

17. SLOPE-INTERCEPT FORM OF A LINE
The slope intercept form of a line is y = mx + b, where “m” represents the slope of the line and “b” represents the y-intercept.
When an equation is in slope-intercept form the “y” is always on one side by itself. It can not be more than one y either.
We have talked about what slope is….
What is a y intercept?

18. Y AND X INTERCEPTS
The y-intercept is the y-coordinate of a point where the graph crosses the y-axis.
The x-intercept is the x-coordinate of a point where the graph crosses the x-axis.
The y-intercept is 3 and is located at the point (0, 3).
The x-intercept would be 4 and is located at the point (4, 0).

19. You can write the slope intercept form of a line….
If you know the slope and the y intercept.
Just substitute them in
Find the slope intercept equation for graphs with the following:
Slope y intercept ½ ¾
Go ahead and do practice D

20. Determine the slope of the line.-1
Find points on the graph.
Use two of them and apply rise over run. 2
The line is decreasing (slope is negative).

21. What is the slope of a horizontal line?
The line doesn’t rise!
All horizontal lines have a slope of 0.

22. What is the slope of a vertical line?
The line doesn’t run!
All vertical lines have an undefined slope.

23. Remember the word “VUXHOY”
Vertical lines
Undefined slope
X = number; This is the equation of the line.
Horizontal lines
O - zero is the slope
Y = number; This is the equation of the line.

24. Complete practice E Identify whether the slope is + or –
Find 2 points on the line
Find the slope by using the rise over run
Give the slope the correct sign
Find the y intercept, what points does the line cross the y axis?
Put the slope and y intercept together to write a slope intercept equation

25. Slope-intercept graphing
Steps
Make sure the equation is in slope-intercept form.
Identify the slope and y-intercept.
Plot the y-intercept.
From the y-intercept use the slope to get another point to draw the line.
y = 3x + 2
Slope = 3 (note that this means the fraction or rise over run could be (3/1) or (-3/-1). The y-intercept is 2.
Plot (0, 2)
From the y-intercept, we are going rise 3 and run 1 since the slope was 3/1.

26. Complete practice F Plot the y intercept
Use rise over run to plot 2 more points
Connect the points
Put an arrow at each end

27. Direct Variations Are linear equations that have a y intercept of 0
These are given a special form y = kx
The k is the same slope, but called the constant of variation
These graphs are easily identified because they always pass through the origin
Complete practice G