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Bellringer August 16 Evaluate the following equations for the given values ๐ฆโ๐ง+๐ฅ๐งรท6;๐ข๐ ๐ ๐ฅ=3, ๐ฆ=4, ๐๐๐ ๐ง=4 ๐ร ๐๐ 4 โ 7โ๐ ;๐ข๐ ๐ ๐=4, ๐=8, ๐๐๐ ๐=5 ๐ฅโ7+ ๐ฅ+๐ง 3 ๐ฅ 6 +3 ;๐ข๐ ๐ ๐ฅ=6 ๐๐๐ ๐ง=3
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Introduction Notes Point Slope form
MAFS.912.F-IF.3.7a
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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
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Slope Formula โ๐ฆ โ๐ฅ = Where ๐ฅ 1 , ๐ฆ 1 ๐๐๐ ( ๐ฅ 2 , ๐ฆ 2 ) are two solutions to the function. Examples ๐ฆ 2 โ ๐ฆ 1 ๐ฅ 2 โ ๐ฅ 1 1. (1,3) and (-2,-11) โ11โ3 โ2โ1 = โ14 โ3 = 14 3 2. (5,-2) and (-5,6) 6โ(โ2) โ5โ5 = 8 โ10 =โ 4 5 3. (8,5) and (-4,4) 5โ4 8โ(โ4) = 1 12
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Write an equation in Point slope form for the following
๐ฆโ ๐ฆ 1 =๐(๐ฅโ ๐ฅ 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= (5, 7) m= (-1,-3) m= 6 8 ๐ฆ+3= 2 3 (๐ฅโ4) ๐ฆ+3= 3 4 (๐ฅ+1) ๐ฆโ7=โ2 (๐ฅโ5)
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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: ๐ฆ+6=โ 2 5 (๐ฅโ2) Plot the given point ( ๐ฅ 1 , ๐ฆ 1 ) โfollowโ the slope
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Examples 4. ๐ฆโ3= 5 2 (๐ฅ+4)
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Examples 5.๐ฆ+4= 2 3 (๐ฅโ3)
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Examples 6. ๐ฆโ4=โ3๐ฅ+6
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Writing an equation in Point Slope form
Step 1:_________________________________ (Reminder: the points are opposite signs. Why?) Step 2:_________________________________ ______________________ or Identify point ( ๐ฅ 1 , ๐ฆ 1 ) on the line Determine slope ๐ฆโ4=โ 5 4 (๐ฅ+4) ๐ฆ+1=โ 5 4 ๐ฅ
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Example ๐ฆโ1=โ(๐ฅ+4) ______________________ or ๐ฆ+1=โ(๐ฅ+2)
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Example ๐ฆ= 1 2 ๐ฅ ______________________ or ๐ฆโ1= 1 2 (๐ฅโ2)
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Example ๐ฆ+4= 1 2 (๐ฅ+1) ______________________ or ๐ฆ+3= 1 2 (๐ฅโ1)
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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 ๐ฆโ3=โ 14 3 (๐ฅโ1) ๐ฆ+2=โ 4 5 (๐ฅโ5) ๐ฆโ5=โ 1 12 (๐ฅโ8) ๐ฆ+11=โ 14 3 (๐ฅ+2) ๐ฆโ6=โ 4 5 (๐ฅ+5) ๐ฆโ4=โ 1 12 (๐ฅ+4)
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Homework: Complete the assigned handout โ
Point Slope Form (Practice Worksheet) Due: Thursday August 17th
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