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 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 DO NOW Consider 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 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 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 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 The steepest street in the world is in Christchurch, New Zealand and has an average slope of 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 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 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 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 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 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 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 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 What is different about this line? = 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 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 Do Question 3 on page 215

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 Consider Example 2 on page 215: To find the slope, you need to find TWO points on the line = = - 8 What does the negative slope mean in this case?

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 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 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 SUMMARY What does the slope of a line measure? What does the slope of a line tell us?