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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)

4)

5)

6)

7)

5 8)

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10)

11)

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6 Scrap Graph Paper

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Work on the following Quiz in your groups: