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

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

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

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

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

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

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

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

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

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

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

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