1. Interpreting Linear Graphs For Real Life Situations

2. Example A Sally paints portraits of people for a living. The graph below shows how much she charges based on how long it takes her to paint the portrait. Sally’s Paintings Charge hours 200 0 50 100 150 01 2 3 4 5

3. Example A (Cont.) What is the slope of this graph? What is the y-intercept? 25 Sally’s Paintings Charge hours 200 0 50 100 150 01 2 3 4 5 50 Rise = 25 Run = 1

4. Example A (Cont.) What does the slope of this graph represent? What does the y-intercept represent? It shows that she charges $25 per hour Sally’s Paintings Charge hours 200 0 50 100 150 01 2 3 4 5 It shows that she has a base fee of $50 in addition to her hourly rate

5. Example A (Cont.) Write an equation for the line in slope-intercept form Write a sentence to explain the equation in terms of the problem. Slope=25 Sally’s Paintings Charge hours 200 0 50 100 150 01 2 3 4 5 Y-int = 50 y = 25x + 50 Sally charges 25 an hour for her painting plus a base fee of 50 for supplies

6. Example A(cont.) How would the graph be different if she made 40 an hour? What would the new equation be if she made 40 an hour? The line would be steeper. (It would go up faster) y = 40x + 50

7. Example A(cont.) How would the graph be different if she did not get a base fee? What would the new equation be if she did not get a base fee The line would start (y-intercept) at 0 instead of 50 or y = 25x y = 25x + 0

8. Example A(cont.) Write an equation for this situation: Sally charges thirty eight dollars an hour for her paintings along with a base fee of 15 dollars for supplies. y = 38x +15 HoursCost 0 1 2 3 4 5 C = 38h +15 15 53 91 129 167 205

9. Example A(Cont.) Sketch the graph Sally’s Paintings Charge hours 200 0 50 100 150 01 2 3 4 5 HoursCost 0 1 2 3 4 5 15 53 91 129 167 205 25 12.5

10. More examples of what slope and y- intercept mean Slope ≈ 4.1667 The slope shows you make about $4.17 per car washed The y-intercept shows starts at $12.50. (Could be a bonus or base wage)

11. More examples Slope = -2500 The slope shows the value of the car decreases 2500 each year The y-intercept shows the value of the car started at 20,000. So maybe the original price was 20,000.

12. More Examples The slope of the income line shows how many dollars they charge for each unit sold. The slope of the expenditure line shows how much it costs them to make each unit. The y-intercept of the income line shows they make $0 for 0 units sold. The y-intercept of the expenditures line shows they spend $250 to start with (Maybe for equipment)

13. Write a Story for Each Equation Y = 3x + 5 A bowling alley charges $3 for each game plus $5 to rent the shoes for the day. Y = 5x – 20 A company sells T-shirts for 5 dollars each but has to pay a 20 equipment fee to use the machine to print them. This equation shows the profit.