1. 7-1 Slope
Objectives: Find the slope of a line given the coordinates of two points on the line

2. What is Slope? Steepness Change in Y Change in X Rise Run
Y=mx + b
Amount of Slant

3. The Graph of y = mx +b Consider the graph of y = x - 2 y5 4 3 2 1 -2 -3 -4 -5 y x
Compare to the graph
of y = ½x - 2
Compare to the graph
of y=2x-2

4. The Graph of y = mx +b Consider the graph of y = x - 2 y5 4 3 2 1 -2 -3 -4 -5 y x
Compare to the graph
of y = -x - 2
Compare to the graph
of y = -2x - 2

5. Determining Slope Rise=1 Rise=12 Run =2 Run =4 Rise=6 Run =2 Slope=

6. Determining Slope Rise= 8 = -2 Rise= 0 Run = -4 Run = n Rise= -2

7. Determining Slope
Rise= n
Run = 0
The Slope is UNDEFINED

8. Determining Slope 5-(-6) = 11 6 2-(-4)
Find the change in the Y-coordinates by subtracting(rise)
Pick 2 points on the line
(2, 5)
Find the change in the X-coordinates by subtracting(run)
5-(-6)
= 11 6
(-4, -6)
2-(-4)
Write as a ratio (rise/run)

9. Determining Slope Y1-Y2 Y2-Y1 m = X1-X2 X2-X1
In general, to find the slope given two points on a line:
Subtract the Y-coordinates (rise)
(x1, y1)
Subtract the X-coordinates (run)
Write as a ratio (rise/run)
(x2, y2)
Y1-Y2
X1-X2
Y2-Y1
m = =
X2-X1

10. Slope Summary Positive Slope Slope = 0 Undefined Slope Negative Slope
Negative slope is a downer
Negative Slope

11. 7-2 Point slope form
Objectives: Write an linear equation in point slope form given the coordinates of a point on the line and the slope of the line

12. Point-Slope form Slope rise/run X coordinate of known point
Y coordinate of known point

13. Point-slope form Write the equation of a line given the point (5,2)
with a slope of 3 m
(x,y)
y–y1=m(x–x1)
Y–2= 3(x–5)

14. 7-3 Writing equations in Slope-Intercept form
Objectives: Write a linear equation in Slope-intercept form given the slope and y intercept

15. Linear Equations (y = mx + b)
b = y-intercept
plot (0,b) to get your first point
m = slope
written as a fraction slope = rise/run
Lean right if positive
Lean left if negative

16. 7-3 y=mx+b Slope intercept form: The y intercept,
Where it crosses the y line
The y coordinate
The x coordinate
Slope rise/run

17. Linear Equations (y = mx + b)
b = -3 (y-intercept)
plot (0,-3)
y = 1/3 x - 3
m = 1/3 (slope rise/run)
positive leans right
plot up 1, right 3
plot down 1, left 3
connect the points

18. Linear Equations (y = mx + b)
b = 2 (y-intercept)
plot (0,2)
y = -1/2 x + 2
m = -1/2 (slope rise/run)
negative leans left
plot up 1, left 2
plot down 1, right 2
connect the points

19. 7-3 Given the slope m and the y intercept b
write an equation in slope intercept form
m= -3
b= -2
Step1: write the equation
y=mx+b
y= -3x-2
Step 2: substitute the given numbers

20. 7-3 The equation can then be graphed y= -3x-2 Rise 3 run to the left 1
m= -3
Fall 3 and run to the right 1

21. 7-3 Subtract the 4x from both sides 4x-2y=8 -4x -4x
Sometimes you may have to manipulate the equation to get it in slope-intercept form
Subtract the 4x from both sides
4x-2y=8
-4x
-4x
Divide all by -2 to isolate y 2 -4
-2y= -4x +8 -2 -2 -2
y=2x-4

22. Given two points, write the equation of a line in y intercept form
(2,-3) and (4,-2)
Steps:
1. Find slope
2. Place a point and the slope in into point slope form
3. Distributive property
4. Additive
property
of equality