1. Unit 5: Analytic Geometry
Minds On
True or False? Explain your Reasoning.
− 1 2 = −1 2 = 1 −2
1 2 𝑥 = 1𝑥 2 = 1𝑥 ÷2 = 1 2𝑥 = 𝑥 2
For

2. Unit 5: Analytic Geometry
Lesson 3: The Equation of a Line
Learning Goals:
I can define slope
I can determine the slope and the y-intercept of a line, given its equation.
I can compare the steepness and direction of lines given their equations
I can calculate the slope of a line from the graph
For

3. Unit 5: Analytic Geometry
Lesson 3: The Equation of a Line
The Equation of a Line is:
y = mx + b
Where m is the slope
And b is the y-intercept

4. Unit 5: Analytic Geometry
Lesson 3: The Equation of a Line
Identify the slope and y-intercept for each of the following:
Y = 2x – 4 y = -3x + 6 y = 9x
Y = 5 – 3x y = 3 4 𝑥+10 y = 5 – 2x
Y = 𝑥 y = 3 −2 𝑥+7 y = -4 - x

5. Unit 5: Analytic Geometry
Lesson 3: The Equation of a Line
What is Slope?
Slope is the measure of the steepness of a line.
Where do we see slopes?

6. Unit 5: Analytic Geometry
Lesson 3: The Equation of a Line
Which hill is steeper?
Hill A: rises 2m over a horizontal run of 8m.
Hill B: rises 4m over a horizontal run of 10m.

7. Unit 5: Analytic Geometry
Lesson 3: The Equation of a Line
We represent slope with the letter “m”.
We can write slope several different ways:
m = slope
Rise: The vertical distance between two points
Run: The horizontal distance between two points
m = 𝑅𝑖𝑠𝑒 𝑅𝑢𝑛
m = 𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑦−𝑣𝑎𝑙𝑢𝑒𝑠 𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑥−𝑣𝑎𝑙𝑢𝑒𝑠
m = ∆𝑦 ∆𝑥
m = 𝑦2−𝑦1 𝑥2−𝑥1

8. Unit 5: Analytic Geometry
Lesson 3: The Equation of a Line
You have already calculated slopes from a graph!

9. Unit 5: Analytic Geometry
Lesson 3: The Equation of a Line
Success Criteria for finding the slope between two points using a graph:
Plot the points
Connect the points with a straight line
Draw a rate triangle between the two points
Count up for the rise
Count across for the run
Put your rise and run into:
Put your rise over run fraction into lowest terms
m = 𝑅𝑖𝑠𝑒 𝑅𝑢𝑛

10. Unit 5: Analytic Geometry
Lesson 3: The Equation of a Line
Example
Success Criteria for finding the slop between two points using a graph:
Plot the points
Connect the points with a straight line
Draw a rate triangle between the two points
Count up for the rise
Count across for the run
Put you rise and run into: m = 𝑅𝑖𝑠𝑒 𝑅𝑢𝑛
Put your fraction in lowest terms B • • A

11. Unit 5: Analytic Geometry
Lesson 3: The Equation of a Line
Use the graph to calculate the slope between the points
(-3, -1) and (4, 3)
Success Criteria for finding the slop between two points using a graph:
Plot the points
Connect the points with a straight line
Draw a rate triangle between the two points
Count up for the rise
Count across for the run
Put you rise and run into: m = 𝑅𝑖𝑠𝑒 𝑅𝑢𝑛
Put your fraction in lowest term

12. Unit 5: Analytic Geometry
Lesson 3: The Equation of a Line
What do you notice about the steepness of each line segment and the speed (a.k.a. slope)

13. Unit 5: Analytic Geometry
Lesson 3: The Equation of a Line
Bigger Slope = Steeper Line
Smaller Slope = Flatter Line

14. Unit 5: Analytic Geometry
Lesson 3: The Equation of a Line

15. Unit 5: Analytic Geometry
Lesson 3: The Equation of a Line
Put the following lines in order from least steep to steepest (Direction does not matter)
Y = 2x – 4 y = -3x + 6 y = 9x
Y = 5 – 3x y = 3 4 𝑥+10 y = 5 – 2x
Y = 𝑥 y = 3 −2 𝑥+7 y = -4 - x

16. Unit 5: Analytic Geometry
Lesson 3: The Equation of a Line
What does the sign (Positive or negative) of the slope tell us?

18. Unit 5: Analytic Geometry
Lesson 3: The Equation of a Line

19. Unit 5: Analytic Geometry
Lesson 3: The Equation of a Line
Positive Slope = Line goes UP to the right
Negative Slope = Lines goes DOWN to the right

20. Unit 5: Analytic Geometry
Lesson 3: The Equation of a Line
State if the line will go up to the right or down to the right
Y = 2x – 4 y = -3x + 6 y = 9x
Y = 5 – 3x y = 3 4 𝑥+10 y = 5 – 2x
Y = 𝑥 y = 3 −2 𝑥+7 y = -4 - x

21. Unit 5: Analytic Geometry
Lesson 3: The Equation of a Line
b in y = mx + b is the y-intercept.
The y-intercept is the point where the line crosses the y-axis.
The x-value of the y-intercept is always:
The y-intercept is also known as:

22. Unit 5: Analytic Geometry
Lesson 3: The Equation of a Line

23. Identify the y-intercepts. The “b”

24. Unit 5: Analytic Geometry
Lesson 3: The Equation of a Line
Practice
Pg. 127 #1 – 5
Pg. 128 #12
Pg. 133 #1-3, 5