Bellringer August 16 Evaluate the following equations for the given values 𝑦−𝑧+𝑥𝑧÷6;𝑢𝑠𝑒 𝑥=3, 𝑦=4, 𝑎𝑛𝑑 𝑧=4 𝑐× 𝑏𝑐 4 − 7−𝑎 ;𝑢𝑠𝑒 𝑎=4, 𝑏=8, 𝑎𝑛𝑑 𝑐=5 𝑥−7+ 𝑥+𝑧 3 𝑥 6 +3 ;𝑢𝑠𝑒 𝑥=6 𝑎𝑛𝑑 𝑧=3

Introduction Notes Point Slope form MAFS.912.F-IF.3.7a

Linear Functions The parent function for all linear functions is f(x)= . All linear functions have critical 3 critical features: 1) where your function crosses the x-axis 2) where your line crosses the y-axis and 3) the slant of your function from one point to the next. x x-intercept y-intercept slope

Slope Formula ∆𝑦 ∆𝑥 = Where 𝑥 1 , 𝑦 1 𝑎𝑛𝑑 ( 𝑥 2 , 𝑦 2 ) are two solutions to the function. Examples 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1 1. (1,3) and (-2,-11) −11−3 −2−1 = −14 −3 = 14 3 2. (5,-2) and (-5,6) 6−(−2) −5−5 = 8 −10 =− 4 5 3. (8,5) and (-4,4) 5−4 8−(−4) = 1 12

Write an equation in Point slope form for the following 𝑦− 𝑦 1 =𝑚(𝑥− 𝑥 1 ) _________________ where m=_________ and x1 and y1 are______________________________. Example: Write an equation in Point slope form for the following Slope Coordinates for a point on the line 1. (4, -3) m= 2 3 2. (5, 7) m= -2 3. (-1,-3) m= 6 8 𝑦+3= 2 3 (𝑥−4) 𝑦+3= 3 4 (𝑥+1) 𝑦−7=−2 (𝑥−5)

Graphing in Point Slope form Steps to graphing in Point slope form: Step 1:_________________________________ (Reminder: the points are opposite signs. Why?) Step 2:_________________________________ Graph the following: 𝑦+6=− 2 5 (𝑥−2) Plot the given point ( 𝑥 1 , 𝑦 1 ) “follow” the slope

Examples 4. 𝑦−3= 5 2 (𝑥+4)

Examples 5.𝑦+4= 2 3 (𝑥−3)

Examples 6. 𝑦−4=−3𝑥+6

Writing an equation in Point Slope form Step 1:_________________________________ (Reminder: the points are opposite signs. Why?) Step 2:_________________________________ ______________________ or Identify point ( 𝑥 1 , 𝑦 1 ) on the line Determine slope 𝑦−4=− 5 4 (𝑥+4) 𝑦+1=− 5 4 𝑥

Example 𝑦−1=−(𝑥+4) ______________________ or 𝑦+1=−(𝑥+2)

Example 𝑦= 1 2 𝑥 ______________________ or 𝑦−1= 1 2 (𝑥−2)

Example 𝑦+4= 1 2 (𝑥+1) ______________________ or 𝑦+3= 1 2 (𝑥−1)

Writing an equation in Point Slope form 10. (1,3) and (-2,-11) __________________ or 11. (5,-2) and (-5,6) __________________ or 12. (8,5) and (-4,4) __________________ or 𝑦−3=− 14 3 (𝑥−1) 𝑦+2=− 4 5 (𝑥−5) 𝑦−5=− 1 12 (𝑥−8) 𝑦+11=− 14 3 (𝑥+2) 𝑦−6=− 4 5 (𝑥+5) 𝑦−4=− 1 12 (𝑥+4)

Homework: Complete the assigned handout – Point Slope Form (Practice Worksheet) Due: Thursday August 17th