This document discusses slope, y-intercept, and how to find and graph linear equations. It defines slope as the ratio that describes a line's tilt and explains how to calculate slope using rise over run between two points on a line. It also discusses how to find the y-intercept, and then use slope and y-intercept to write the equation of a line in y=mx+b form. Examples are provided for finding slope from tables of values and graphing linear equations on a coordinate plane.

1. March 24, 2011
SLOPE AND Y-INTERCEPT

2. What is slope?
 The slope of a line is the ratio that describes
its tilt.
 The slope of a line can be:
Positive Negative

3. What is slope?
Zero Undefined

4. How do we find the slope?
1. Find two points on the line with coordinates
that are easy to read.

5. How do we find the slope?
2. Between these two points, find the rise (the
change in y going up or down) and the
run(the change in x going left or right) .
Rise=3
Run= 4

6. How do we find the slope?
3. To find the slope, divide the rise by the run.
Rise=3
Run= 4

7. STOP
Now, work problems 1 and 2 on the Reteaching
8-3 worksheet.
Answer to #1: -3
Answer to #2: -5/2

8. Another way to find the slope
 We can also find the slope using only the
coordinates of the two points.
 Suppose we have points A (4,5) and B (0,2).
 To find the slope, find the difference between
the y-coordinates of A and B (the rise) and
divide it by the difference between the x-
coordinates (the run).

9. STOP
Now, work problems 3 and 6 on the Reteaching
8-3 worksheet.
Answer to #3: 1/4
Answer to #6: 3

10. Finding the equation of a line
 Now that we know the slope of our line, we
can find its equation using slope-intercept
form.
 But before we can do this, we must find the y-
intercept of the line.
 Y-intercept= the value of y when x is zero

11. Finding the equation of a line
 To find the y-intercept, follow the y-axis
upward or downward until you reach the line.
Y-intercept
=2

12. Finding the equation of a line
 Now that we know the slope and y-intercept,
we use this equation:
y = mx + b
where m is the slope and b is the y-intercept.
Since our slope was m=3/4 and our y-intercept
was b=2, the equation of our line is:
y= ¾ x + 2.

13. STOP
Now, work problem #1 on the Practice 8-4
worksheet.
Answer to #1: y = -5/4 x + 2

14. Graphing Linear Equations
Now that we know y= mx + b, we can graph
linear equations much more easily.
Let’s try the equation: y= 2/3 x + 1
1. Identify m(slope) and b(y-intercept).
In this case, m= 2/3 and b= 1.

15. Graphing Linear Equations
2. Place a point at (0, b). An easy way to
remember this is that b is for begin. In this
case, that would be the point (0,1).

16. Graphing Linear Equations
3. Now, use the slope to plot another point. We
know that our slope is 2/3, so we want to go
up 2 units and 3 units to the right.

17. Graphing Linear Equations
4. Next, connect the two points with a ruler or
straightedge, extending the line in both
directions.

18. STOP
Work problem 9 on the Practice 8-3 worksheet.
Answer to #9:

19. Writing a Linear Equation from a
Table
 Suppose you are given a table like this:
x y
-2 -11
0 -5
2 1
4 7

20. Writing a Linear Equation from a
Table
1. First, look for a pattern on each side of the
table. For this table, we notice:
x y
-2 -11 +6
+2
0 -5
+2 +6
2 1
+2 +6
4 7

21. Writing a Linear Equation from a
Table
2. Next, divide the change in y by the change in
x to get the slope. In this case,
3. To find the y-intercept, we simply look at the
table and find the value of y when x=0. In this
case, y= -5.

22. Writing a Linear Equation from a
Table
4. Now that we have m=3 and b= -5, we can
plug these values into y= mx + b to get our
equation.
So we have y= 3x – 5.

23. STOP
Now, work problems 1 and 2 from the
Reteaching 8-4 worksheet.
Answer to #1: y= 7x
Answer to #2: y= x - 8

24. THE END
Have a wonderful day!