1. Meaning of Slope for Equations, Graphs, and Tables
Section 1.4
Meaning of Slope for Equations, Graphs, and Tables

2. Find the slope of the line
Finding Slope from a Linear Equation
Finding Slope from a Linear Equation
Example
Find the slope of the line
Solution
x y 3 5
Create a table using x = 1, 2, Then sketch the graph.
Section 1.4
Slide 2

3. Note the following three observations about the slope of the line
Finding Slope from a Linear Equation
Finding Slope from a Linear Equation
Observations
Note the following three observations about the slope of the line
The coefficient of x is 2, which is the slope.
If the run is 1, then the rise is 2.
As the value of x increases by 1, the value of y increases by 2.
Section 1.4
Slide 3

4. Find the slope of the line
Finding Slope from a Linear Equation
Finding Slope from a Linear Equation
Example
Find the slope of the line
Solution
x y 5 2
3 –1
Create a table using x = 1, 2, Then sketch the graph.
Section 1.4
Slide 4

5. For the line , if the run is 1, then the rise is m.
Vertical Change Property
Vertical Change Property
Property
For the line , if the run is 1, then the rise is m.
Vertical Change property for a positive slope.
Vertical Change property for a negative slope.
Section 1.4
Slide 5

6. Finding the y-intercept of a Linear Line
Finding the y-Intercept of linear Equation
Sketching Equations:
It’s helpful to know the y-intercept.
y-intercept has a x-value of 0.
Substitute x = 0 gives
Property
For a linear equation of the form , the y- intercept is (0, b).
Section 1.4
Slide 6

7. What is the y-intercept of
Finding the y-intercept of a Linear Line
Finding the y-Intercept of linear Equation
Example
What is the y-intercept of
Solution
b is equal to 3, so the y-intercept is (0, 3)
Definition
If an equation of the form , we say that it is in slope-intercept form.
Section 1.4
Slide 7

8. Graphing Linear Equations
Example
Sketch the graph of y = 3x – 1.
Solution
The y-intercept is (0, –1) and the slope is
To graph:
Plot the y-intercept, (0, 1) (continued)
Section 1.4
Slide 8

9. Graphing Linear Equations
Solution Continued
From (0, –1), look 1 unit to the right and 3 units up to plot a second point, which we see by inspection is (1, 2).
Sketch the line that contains these two points.
Section 1.4
Slide 9

10. Graphing Linear Equations
Guidelines
To sketch the graph of a linear equation of the form
Plot the y-intercept (0, b).
Use m = to plot a second point.
Sketch the line that passes through the two plotted points.
Section 1.4
Slide 10

11. Graphing Linear Equations
Example
Sketch the graph of 2x + 3y = 6.
Solution
First we rewrite into slope-intercept form:
Original Equation
Subtract 2x from both sides.
Combine & rearrange terms
Divide both sides by 3.
Section 1.4
Slide 11

12. Graphing Linear Equations
Solution Continued
y-intercept: (0, 2) Slope:
Plot the y-intercept, (0, 2).
2. From the point (0, 2), look 3 units to the right and 2 units down to plot a second point, which we see by inspection is (3, 0).
Section 1.4
Slide 12

13. Graphing Linear Equations
Solution Continued
3. Then sketch the line that contains these two points. We can verify our result by checking that both (0, 2) and (3, 0) are solutions.
Section 1.4
Slide 13

14. Slope Addition Property
Example
For the following sets, is there a line that passes through them? If so, find the slope of that line.
Solution
Value of x increases by 1.
Value of y changes by –3.
The slope is –3.
Section 1.4
Slide 14

15. Slope Addition Property
Solution Continued
Set 2
Value of x increases by 1.
Value of y changes by 5.
So, the slope is 5.
Set 3
Value of y does not change by the same value. Hence, not a line.
Section 1.4
Slide 15