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 a linear equation of the form , m is the slope of the line.
Finding Slope from a Linear Equation
Finding Slope from a Linear Equation
Property
For a linear equation of the form , m is the slope of the line.
Example
Are the lines parallel,
perpendicular, or neither?
Section 1.4
Slide 5

6. For the line the slope is For the other equation we solve for y:
Finding Slope from a Linear Equation
Finding Slope from a Linear Equation
Property
For the line the slope is
For the other equation we solve for y:
Original Equation
Add 10x to both sides.
Combine & rearrange terms
Divide both sides by 12.
Simplify.
Section 1.4
Slide 6

7. Finding Slope from a Linear Equation
Solution Continued
For the line the slope is
Since the slopes are the same for both equations, the lines are parallel
Graphing Calculator
We use ZStandard followed by ZSquare to draw the line in the same coordinate system.
Section 1.4
Slide 7

8. 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 8

9. 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 9

10. 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 10

11. 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 11

12. 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 12

13. 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 13

14. 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 14

15. 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 15

16. 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 16

17. Graphing Linear Equations
Example
Determine the slope and the y-intercept of ax + by =c, where a, b, and c are constants and b is nonzero.
2. Find the slope and the y-intercept of the graph of 3x + 7y = 5.
Solution
First we rewrite into slope-intercept form:
Section 1.4
Slide 17

18. Graphing Linear Equations
Solution Continued
Slope is and the y-intercept is
Section 1.4
Slide 18

19. Graphing Linear Equations
Solution Continued
Given that ax + by = c in slope-intercept form is
, then given 3x + 7y = 5, we substitute .
3 for a, 7 for b and 5 for c. Thus, the slope,
Section 1.4
Slide 19

20. 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 20

21. 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 21