1. 20S Applied Math Mr. Knight – Killarney School Slide 1 Unit: Real Number System Lesson: LMP-L2 Characteristics of a Linear Function Characteristics of the Graph of a Linear Function Learning Outcome B-4 LMP-L2 Objectives: To calculate the equation of a linear function.

2. 20S Applied Math Mr. Knight – Killarney School Slide 2 Unit: Real Number System Lesson: LMP-L2 Characteristics of a Linear Function In this lesson, you will: Review how to calculate the slope of a line. Review how to determine the y-intercept of a line. Determine the equation of a line from raw data (tables of values) or written descriptions. Objectives

3. 20S Applied Math Mr. Knight – Killarney School Slide 3 Unit: Real Number System Lesson: LMP-L2 Characteristics of a Linear Function Suppose you are tracking the motion of an object that is moving at a constant speed. You obtain a table of values that looks like this: Example 1 – Slope review A graph of the situation is: The line’s rise is the object’s change in distance. The line’s run is its change in time. The slope, therefore, is its speed (distance/time).

4. 20S Applied Math Mr. Knight – Killarney School Slide 4 Unit: Real Number System Lesson: LMP-L2 Characteristics of a Linear Function The motion of an object has been recorded and the data is shown in the table below: Example 2 – Slope review Sketch a graph of the data Find the slope of the line segments: AC, BE and BF. What do the slope values represent? ALL 3 slopes simplify to 150 m/s. The slope, again, describes speed (distance/time).

5. 20S Applied Math Mr. Knight – Killarney School Slide 5 Unit: Real Number System Lesson: LMP-L2 Characteristics of a Linear Function The cost of producing a school yearbook is $1000 for setup fees and $1200 for each lot of 100 copies purchased. Here is a table of values showing the total cost for 100, 200, 300, or 400 copies purchased. Example 3 – Y-Intercept Review A graph of the data is shown The red line shows the line of best fit through the points. It is extended to intersect the y-axis at the point B. The coordinates of B are: (0, 1000). This point is the y-intercept of the line ( b = 1000). This represents the startup cost.

6. 20S Applied Math Mr. Knight – Killarney School Slide 6 Unit: Real Number System Lesson: LMP-L2 Characteristics of a Linear Function The graph shows the cost of taking a taxi for various distances. What is the significance of the y-intercept A? Example 4.a – Equation of a Line The coordinates of the point A are (0, 4). This means that before you have traveled any distance the cost is $4.00. The startup cost of taking the taxi is $4.00.

7. 20S Applied Math Mr. Knight – Killarney School Slide 7 Unit: Real Number System Lesson: LMP-L2 Characteristics of a Linear Function The graph shows the cost of taking a taxi for various distances. What is the slope of the line? Example 4.b – Equation of a Line

8. 20S Applied Math Mr. Knight – Killarney School Slide 8 Unit: Real Number System Lesson: LMP-L2 Characteristics of a Linear Function The graph shows the cost of taking a taxi for various distances. Example 4.c – Equation of a Line What is the equation of the line in the form y = mx + b. The equation is y = 1x + 4, where y represents the cost in $ and x represents the distance traveled by the taxi in km. What is the cost of a 10 km trip? The cost of a 10 km trip will be 1(10) + 4 or $14. How far could you travel for $6.25? Use the equation, y = 1x + 4, where y would be $6.25 and solve for x. You can travel 2.25 km.

9. 20S Applied Math Mr. Knight – Killarney School Slide 9 Unit: Real Number System Lesson: LMP-L2 Characteristics of a Linear Function In testing the effectiveness of a new antibacterial spray, a biochemist recorded the number of bacteria present in a tissue culture after the spray had been present for different periods of time. The data are recorded in the table below: Example 5 – Full Analysis a) Find the slope. What does the negative quantity mean? b) Find the y-intercept. What does it represent? c) Write the equation of the line. d) After how many hours would 25 bacteria be present? e) State the largest value and the smallest value of the domain. f) State the largest value and the smallest value of the range.

10. 20S Applied Math Mr. Knight – Killarney School Slide 10 Unit: Real Number System Lesson: LMP-L2 Characteristics of a Linear Function Example 5 – Full Analysis a.The slope is -5. The negative quantity means that the number of bacteria is decreasing instead of increasing. b.The y-intercept is 100. That means you started with 100 bacteria at time 0. c.Using the equation y = mx + b, and substituting the values for m and b, you will get: y = -5x + 100. d.Twenty five bacteria represents a y-value. Substitute 25 for y, and solve the equation for x. (Use Winplot if you want). x = 15 hours. After 15 h, there will be 25 bacteria. e.The domain is the set of x-values for our graph {0 ≤ x ≤ 20} f.The range is the set of y-values for our graph {0 ≤ y ≤ 100}