semester b day 1 lesson 5-1 aim: to use counting units to find the slope of a line standards 4a:...
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Semester B Day 1 Lesson 5-1
Aim: To use counting units to find the slope of a line
Standards 4A: Represent problem situations symbolically by using graphs
5G: Relate absolute value, distance between two points and the slope of a line to the coordinate plane
Key terms: equations of a line; point –slope and slope intercept form
Semester B Day 1 Lesson 5-1
Aim: To use counting units to find the slope of a lineStandards 4A: Represent problem situations symbolically by using graphs
5G: Relate absolute value, distance between two points and the slope of a line to the coordinate plane
Key terms: equations of a line; point –slope and slope intercept form
DO NOWConsider the following graph that indicates how you should alter your
training heart rate with age.
What information does it give you about training heart rate and age?
What does it mean when we talk about the ‘slope of a line’?
What are some other things that vary in slope?
Semester B Day 1 Lesson 5-1
Aim: To use counting units to find the slope of a lineStandards 4A: Represent problem situations symbolically by using graphs
5G: Relate absolute value, distance between two points and the slope of a line to the coordinate plane
Key terms: equations of a line; point –slope and slope intercept form
Objective: To learn how to calculate the slope of a line
The slope of a line is the same as the ‘steepness’ of the line.
Carpenters use the terms rise and run to describe the steepness of stairs or a roof line.
Steepness or slope = rise run
Semester B Day 1 Lesson 5-1
Aim: To use counting units to find the slope of a lineStandards 4A: Represent problem situations symbolically by using graphs
5G: Relate absolute value, distance between two points and the slope of a line to the coordinate plane
Key terms: equations of a line; point –slope and slope intercept form
The steepest street in the world is in Christchurch, New Zealand and has an average slope of 1.266. This doesn’t sound very steep until you see it.
Semester B Day 1 Lesson 5-1
Aim: To use counting units to find the slope of a lineStandards 4A: Represent problem situations symbolically by using graphs
5G: Relate absolute value, distance between two points and the slope of a line to the coordinate plane
Key terms: equations of a line; point –slope and slope intercept form
How can you make a model to show how steep this street is?
Do this exercise in a group.
Semester B Day 1 Lesson 5-1
Aim: To use counting units to find the slope of a lineStandards 4A: Represent problem situations symbolically by using graphs
5G: Relate absolute value, distance between two points and the slope of a line to the coordinate plane
Key terms: equations of a line; point –slope and slope intercept form
Consider the following pictures:
1.Which hill appears to be the steepest?
Give an explanation for your answer
2. Work out the actual steepness or slope of each hill.
Semester B Day 1 Lesson 5-1
Aim: To use counting units to find the slope of a lineStandards 4A: Represent problem situations symbolically by using graphs
5G: Relate absolute value, distance between two points and the slope of a line to the coordinate plane
Key terms: equations of a line; point –slope and slope intercept form
Remember that the slope of a line = rise = vertical change run horizontal change
= 2 5
So the slope of the line is 2 5
Semester B Day 1 Lesson 5-1
Aim: To use counting units to find the slope of a lineStandards 4A: Represent problem situations symbolically by using graphs
5G: Relate absolute value, distance between two points and the slope of a line to the coordinate plane
Key terms: equations of a line; point –slope and slope intercept form
What is different about this line?
= - 3 5
So the slope of the line is – 3 5
We ‘read’ slopes from left to right. So if a line slopes down from left to right it has a negative slope.
Semester B Day 1 Lesson 5-1
Aim: To use counting units to find the slope of a lineStandards 4A: Represent problem situations symbolically by using graphs
5G: Relate absolute value, distance between two points and the slope of a line to the coordinate plane
Key terms: equations of a line; point –slope and slope intercept form
Do Question 3 on page 215
Semester B Day 1 Lesson 5-1
Aim: To use counting units to find the slope of a lineStandards 4A: Represent problem situations symbolically by using graphs
5G: Relate absolute value, distance between two points and the slope of a line to the coordinate plane
Key terms: equations of a line; point –slope and slope intercept formConsider Example 2 on page 215:
To find the slope, you need to find TWO points on the line
= -1000 120
= - 8
What does the negative slope mean in this case?3
1
Semester B Day 1 Lesson 5-1
Aim: To use counting units to find the slope of a lineStandards 4A: Represent problem situations symbolically by using graphs
5G: Relate absolute value, distance between two points and the slope of a line to the coordinate plane
Key terms: equations of a line; point –slope and slope intercept form
Do Question 4 on page 215
Homework: Complete Questions 1, 3, 4, 7, 20, 22, 23, 24 on page 217
Semester B Day 1 Lesson 5-1
Aim: To use counting units to find the slope of a lineStandards 4A: Represent problem situations symbolically by using graphs
5G: Relate absolute value, distance between two points and the slope of a line to the coordinate plane
Key terms: equations of a line; point –slope and slope intercept form
SUMMARY
What does the slope of a line measure?
What does the slope of a line tell us?