1. Activating Prior Knowledge – Notes
M4:LSN23
The Defining Equation of a Line
Activating Prior Knowledge – Notes
What is the slope and y-intercept of the following line?
3y = 6x + 9
𝒎=𝟐, 𝒃=𝟑
Find the slope using the given points.
(3,4) (12, 13)
𝒎= 𝟏𝟑−𝟒 𝟏𝟐−𝟑 =
𝟗 𝟗 =𝟏
Tie to LO

2. Learning Objective
Today, we will understand that an equation written in standard form can also be written in slope-intercept form.
CFU

3. Concept Development Review
M4:LSN22
M4:LSN23
Concept Development Review
The Defining Equation of a Line
Concept Development
Graph the equation 𝟗𝒙+𝟑𝒚=𝟏𝟖 using intercepts.
Find y intercept
𝟗 𝟎 +𝟑𝒚=𝟏𝟖 𝟑𝒚=𝟏𝟖 𝒚=𝟔
The 𝒚-intercept is 𝟎, 𝟔 .
Find x intercept
𝟗𝒙+𝟑 𝟎 =𝟏𝟖 𝟗𝒙=𝟏𝟖 𝒙=𝟐
The 𝒙-intercept is (𝟐, 𝟎).
CFU

4. Concept Development Continued
M4:LSN23
The Defining Equation of a Line
Concept Development Continued
Graph the equation 𝒚=−𝟑𝒙+𝟔 on the same coordinate plane.
What do you notice about the graphs of 𝟗𝒙+𝟑𝒚=𝟏𝟖 and 𝒚=−𝟑𝒙+𝟔? Why do you think this is so?
The graphs of the equations produce the same line. Both equations go through the same two points so they are the same line.
CFU

5. Concept Development Continued
M4:LSN23
The Defining Equation of a Line
Concept Development Continued
Rewrite 𝒚=−𝟑𝒙+𝟔 in standard form.
ax + by = c
𝒚=−𝟑𝒙+𝟔
+ 3x
+ 3x
𝟑𝒙+𝒚=𝟔
Identify the constants, 𝒂, 𝒃, 𝒄 of the equation in standard form from part (c).
𝒂=𝟑, 𝒃=𝟏, and 𝒄=𝟔.
CFU

6. Concept Development CFU The Defining Equation of a Line
M4:LSN23
The Defining Equation of a Line
Concept Development
Graph the equation 𝒚= 𝟏 𝟐 𝒙+𝟑 using the 𝒚-intercept and the slope.
Now, graph the equation 𝟒𝒙−𝟖𝒚=−𝟐𝟒 using intercepts on the same coordinate plane.
𝟒 𝟎 −𝟖𝒚=−𝟐𝟒 −𝟖𝒚=−𝟐𝟒 𝒚=𝟑
The 𝒚-intercept is 𝟎, 𝟑 .
𝟒𝒙−𝟖 𝟎 =−𝟐𝟒 𝟒𝒙=−𝟐𝟒 𝒙=−𝟔
The 𝒙-intercept is −𝟔, 𝟎 .
What do you notice about the graphs of 𝒚= 𝟏 𝟐 𝒙+𝟑 and 𝟒𝒙−𝟖𝒚=−𝟐𝟒?
The graphs of the equations produce the same line. Both equations go through the same two points, so they are the same line.
CFU

7. Concept Development CFU The Defining Equation of a Line
M4:LSN23
The Defining Equation of a Line
Concept Development
Rewrite 𝒚= 𝟏 𝟐 𝒙+𝟑 in standard form
𝒚= 𝟏 𝟐 𝒙+𝟑
𝒚= 𝟏 𝟐 𝒙+𝟑 𝟐
𝟐𝒚=𝒙+𝟔
−𝒙+𝟐𝒚=𝟔
−𝟏 −𝒙+𝟐𝒚=𝟔
𝒙−𝟐𝒚=−𝟔
Multiply by 2 to eliminate the fraction.
Subtract x from both sides
Multiply entire equation by -1 so x is positive.
CFU

8. Skill Development/Guided Practice
M4:LSN23
The Defining Equation of a Line
Skill Development/Guided Practice
𝒙−𝟐𝒚=−𝟔
Identify the constants, 𝒂, 𝒃, 𝒄 of the equation in standard form.
𝒂=𝟏, 𝒃=−𝟐, and 𝒄=−𝟔.
Identify the constants of the equation
𝟒𝒙−𝟖𝒚=−𝟐𝟒.
𝒂 =𝟒, 𝒃 =−𝟖, and 𝒄 =−𝟐𝟒
CFU

9. Skill Development/Guided Practice
M4:LSN23
The Defining Equation of a Line
Skill Development/Guided Practice
The equations 𝒚= 𝟐 𝟑 𝒙−𝟒 and 𝟔𝒙−𝟗𝒚=𝟑𝟔 graph as the same line.
𝒚= 𝟐 𝟑 𝒙−𝟒 𝒚= 𝟐 𝟑 𝒙−𝟒 𝟑 𝟑𝒚=𝟐𝒙−𝟏𝟐 −𝟐𝒙+𝟑𝒚=−𝟏𝟐 −𝟏 −𝟐𝒙+𝟑𝒚=−𝟏𝟐 𝟐𝒙−𝟑𝒚=𝟏𝟐
Identify the constants, 𝒂, 𝒃, 𝒄, of the equation in standard form.
𝒂=𝟐, 𝒃=−𝟑, and 𝒄=𝟏𝟐.
CFU

10. Skill Development/Guided Practice
M4:LSN5
The Defining Equation of a Line
Skill Development/Guided Practice
Write three equations that would graph as the same line as the equation 𝟑𝒙+𝟐𝒚=𝟕.
CFU

11. Skill Development / Guided Practice
M4:LSN23
Writing and Solving Linear Equations
Skill Development / Guided Practice
Write at least two equations in the form 𝒂𝒙+𝒃𝒚=𝒄 that would graph as the line shown below.
CFU

12. Closure CFU 1. What did we learn today?
2. Why is this important to you?
3. What is the standard form of the equation of a line?
4. What is the slope formula?
5. What is the slope – intercept form of a line?
Homework:
Problem Set 1 – 3 and study for tomorrow’s quiz on lessons 20 – 22.
CFU