Unit 5: Analytic Geometry
Minds On
True or False? Explain your Reasoning.
a) = =
b) = = = =
Unit 5: Analytic Geometry
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
Lesson 3: The Equation of a Line
Unit 5: Analytic Geometry
Lesson 3: The Equation of a Line
The Equation of a Line is:
y = mx + b
Where m is the slopeAnd b is the y-intercept
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 = y = 5 – 2x
Y = -9 + y = y = -4 - x
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?
Unit 5: Analytic Geometry
Which hill is steeper?
Hill A: rises 2m over a horizontal run of 8m.
Hill B: rises 4m over a horizontal run of 10m.
Lesson 3: The Equation of a Line
Unit 5: Analytic Geometry
We represent slope with the letter “m”.We can write slope several different ways:
m = slopem =
m =
m =
m =
Rise: The vertical distance between two points
Run: The horizontal distance between two points
Lesson 3: The Equation of a Line
Unit 5: Analytic Geometry
You have already calculated slopes from a graph!
Lesson 3: The Equation of a Line
Unit 5: Analytic Geometry
Success Criteria for finding the slope between two points using a graph:
Plot the pointsConnect the points with a straight lineDraw a rate triangle between the two
pointsCount up for the riseCount across for the runPut your rise and run into:Put your rise over run fraction into
lowest terms
m =
Lesson 3: The Equation of a Line
Unit 5: Analytic Geometry
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 = Put your fraction in
lowest terms•
•
A
B
Lesson 3: The Equation of a Line
Unit 5: Analytic Geometry
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 = Put your fraction in
lowest term
Lesson 3: The Equation of a Line
Unit 5: Analytic Geometry
What do you notice about the steepness of each line segment and the speed (a.k.a. slope)
Lesson 3: The Equation of a Line
Unit 5: Analytic Geometry
Bigger Slope = Steeper Line
Smaller Slope = Flatter Line
Lesson 3: The Equation of a Line
Unit 5: Analytic Geometry
Lesson 3: The Equation of a Line
https://www.desmos.com/calculator/1rf9v33t86
Unit 5: Analytic Geometry
Put the following lines in order from least steep to steepest (Direction does not matter)
Lesson 3: The Equation of a Line
Y = 2x – 4 y = -3x + 6 y = 9x
Y = 5 – 3x y = y = 5 – 2x
Y = -9 + y = y = -4 - x
Unit 5: Analytic Geometry
What does the sign (Positive or negative) of the slope tell us?
Lesson 3: The Equation of a Line
Unit 5: Analytic Geometry
Lesson 3: The Equation of a Line
https://www.desmos.com/calculator/1rf9v33t86
Unit 5: Analytic Geometry
Positive Slope = Line goes UP to the right
Negative Slope = Lines goes DOWN to the right
Lesson 3: The Equation of a Line
Unit 5: Analytic Geometry
State if the line will go up to the right or down to the right
Lesson 3: The Equation of a Line
Y = 2x – 4 y = -3x + 6 y = 9x
Y = 5 – 3x y = y = 5 – 2x
Y = -9 + y = y = -4 - x
Unit 5: Analytic Geometry
b in y = mx + b is the y-intercept.
Lesson 3: The Equation of a Line
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:
Unit 5: Analytic Geometry
Lesson 3: The Equation of a Line
https://www.desmos.com/calculator/1rf9v33t86
Identify the y-intercepts. The “b”
Unit 5: Analytic Geometry
Practice
Pg. 127 #1 – 5 Pg. 128 #12
Pg. 133 #1-3, 5
Lesson 3: The Equation of a Line