1. Stand Quietly

2. Lesson 6.3_Linear Function
Students will be able to use a function to describe a linear pattern.
CCSS. 8.F.2, F.3, F.4

3. Warm-Up #18 (4/6/2017) Which mapping represents a function
Write a function notation for this statement: the output is four times the input.
Write a sentence for y=5x-3

4. Homework (4/6/2017)
Workbook: Record and Practice Journal Page 132

5. YouTube

6. A linear function is a function whose graph is a nonvertical
A linear function is a function whose graph is a nonvertical. A linear function can be written in standard form (Ax+By=C), slope-intercept form (y=mx+b) and point slope form (y− 𝑦 1 )=𝑚(𝑥− 𝑥 1 ).

7. For the purpose of this Chapter we will have the linear function be written in the form y=mx+b, where m is the slope and b is the y-intercept.

8. For each problem, explain why it is a linear function or it is not a linear function
𝑓 𝑥 =3𝑥−2
𝑓 𝑥 = 𝑥 2 −4
𝑓 𝑥 = 1 2 𝑥
𝑓 𝑥 = 𝑥 3 −𝑥
𝑓 𝑥 =3
Yes because the slope is 3 and the y-intercept is -2
No, the x has a power of 2
Yes because the slope is ½ and the y-intercept is 0
No, there are more than two x variables with
different powers
Yes because the slope is 0 and the y-intercept is 3

9. Average Rate of Change (Slope)
The average rate of change of a Linear Function is the constant
For example, f(x)= 5x - 2 , the average rate of change is m = 5

10. f(x) = -3x+4 The slope is m = -3, the y-intercept b = 4
The average rate of change is the constant m = -3
Since m = -3 is negative. The graph is slanted downwards. Thus the function is decreasing

11. f(x) = 3 f(x)=0x + 3 m = 0 b = 3 The average rate of change is 0
Since the average rate of change, m = 0
The function is constant neither increasing or decreasing

12. 𝑺𝒍𝒐𝒑𝒆 𝒇𝒐𝒓𝒎𝒖𝒍𝒂: 𝒎= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏 = ∆𝒚 ∆𝒙
𝑺𝒍𝒐𝒑𝒆 𝒇𝒐𝒓𝒎𝒖𝒍𝒂: 𝒎= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏 = ∆𝒚 ∆𝒙
Table #1
pick two points
(2,1) and (5, 3)
𝒎= 𝟑−𝟏 𝟓−𝟐
𝒎= 𝟐 𝟑

13. 𝑺𝒍𝒐𝒑𝒆 𝒇𝒐𝒓𝒎𝒖𝒍𝒂: 𝒎= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏 = ∆𝒚 ∆𝒙
𝑺𝒍𝒐𝒑𝒆 𝒇𝒐𝒓𝒎𝒖𝒍𝒂: 𝒎= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏 = ∆𝒚 ∆𝒙
Table #2
pick two points
(1,10) and (2, 13)
𝒎= 𝟏𝟑−𝟏𝟎 𝟐−𝟏
𝒎= 𝟑 𝟏 =𝟑

14. 𝑺𝒍𝒐𝒑𝒆 𝒇𝒐𝒓𝒎𝒖𝒍𝒂: 𝒎= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏 = ∆𝒚 ∆𝒙
𝑺𝒍𝒐𝒑𝒆 𝒇𝒐𝒓𝒎𝒖𝒍𝒂: 𝒎= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏 = ∆𝒚 ∆𝒙
Table #3
pick two points
(2,1) and (4, 6)
𝒎= 𝟔−𝟏 𝟒−𝟐
𝒎= 𝟓 𝟐