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Lesson Plan #69
Class: Geometry Date: Tuesday March 10th, 2020
Topic: Equation of a line. Aim: How can we graph a line given its equation?
Objectives:
1) Students will be able to graph a linear equation.
HW #69:
Do Now:
1) Solve the equation: 5(𝑥 − 5)2 = 45. Then check your answers.
PROCEDURE:
Write the Aim and Do Now
Get students working! Take attendance Give Back HW
Collect HW
Go over the Do Now
Assignment #1:
A) Is 𝑥 = 3, 𝑦 = 1 a solution to the equation 𝑥 + 9𝑦 = 12?
B) Is 𝑥 = 0, 𝑦 =4
3 a solution to the equation 𝑥 + 9𝑦 = 12?
C) Aside from (3,1), and (0,4
3)find another solution to equation 𝑥 + 9𝑦 = 12.
D) Graph the points that are solutions to the equation 𝑥 + 9𝑦 = 12. What figure do you get when you graph all the solutions
to𝑥 + 9𝑦 = 12?
Assignment #2:
Find 3 solutions to the equation 𝑦 =2
3𝑥 + 1. Graph the line whose equation is 𝑦 =
2
3𝑥 + 1
What is the slope of the line?
What is the y-intercept of the line?
Theorem: An equation of a line whose slope is 𝑚 and whose 𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 is 𝑏𝑦 = 𝑚𝑥 + 𝑏
2 Interactive Online Activity:
http://www.geogebra.org/en/upload/files/english/Athena_Matherly/Slope_Intercept_Form/slope_intercept_form.html
Example #1:
Write an equation of a line whose
A) slope is 4 and whose 𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 is 5
B) slope is 2 and whose 𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 is -5
C) slope is -7 and whose 𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 is 0
D) slope is 0 and whose 𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 is 0
Example #2:
Find the slope and 𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 of each of the following
A) 𝑦 = 3𝑥 + 1 Slope = 𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 =
B) 2𝑥 + 𝑦 = 9 Slope = 𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 =
Example #3:
A) Write an equation of a line whose slope 3 and passes through the point (1,5).
B) Write an equation of a line show slope is 2
3 and passes through the point (−1,4).
Example #4:
Write an equation of a line that passes through the points
A) (1,5) and (5,13)
B) (−4, −1)and (−1,11)
Example 5 :
Write an equation of a line that is
A) parallel to 𝑦 = 3𝑥 − 5 and whose 𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 is 7
B) parallel to 2𝑦 − 4𝑥 = 9 and passes through the point (−2,1)
C) perpendicular to 𝑦 =3
4𝑥 + 7 and passes through the origin.
Interactive Online Activity: Let’s discover the point slope form of a line. Let’s go to
http://www.geogebra.org/en/upload/files/english/Athena_Matherly/Point_Slope_Form/point_slope_form_WS.html
Theorem: An equation of a line passing through the poitn (𝑥1, 𝑦1)and having slope 𝑚 is 𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1)
Example #6: Write an equation of a line, in point-slope form, that has slope 2 and passes through the piont (2,3)
Example #7: Write an equationof a line, in point-slope form, that passes through the points (-1,-2) and (5,1).
3
Cominbe what we’ve done earlier in the term with equation of a line
1) Sketch the graph of 2 2
3 1 36x y
A) Is the point with coordinates 8, 4 on the
circle, inside the circle or outside the circle?
Justify your answer.
B) Write an equation of the line tangent to
the circle at 3, 7 .
C) Write an equation of the line tangent to
the circle at 9,1 .
D) Write an equation of the line that passes
through the points 3, 7 and 9,1 .
E) Inscribe an equilateral triangle in the circle. F) Find the area of circle.
2) A) Find an equation of the line that coincides with BC .
B) Write an equation of a line that coincides with the perpendicular bisector of BC .
C) Construct the perpendicular bisector of AB .
D) Draw in the midsegment that is parallel to AC .
E) Find the equation of AC .
F) Construct the circumcircle of ABC .
G) Write the equation of the circumcircle.
H) Find the area of ABC
4 Group Work: Answer the past regents questions with your group, justifying your solutions with deductive reasoning.
1)
2)
3)
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5)
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5 8)
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6 Scrap Graph Paper
7
Work on the following Quiz in your groups: