Activating Prior Knowledge – Notes M4:LSN17 The Line Joining Two Distinct Points of the Graph y = mx + b has Slope m. Activating Prior Knowledge – Notes Draw the following. 1. negative slope 2. undefined slope 3. positive slope 4. zero slope Tie to LO

Learning Objective Today, we will show that the slope of a line given by the equation 𝒚= 𝒎𝒙+𝒃, is 𝒎. CFU

CFU Topic C: Slope and Equations of Lines M4:LSN17 The Line Joining Two Distinct Points of the Graph y = mx + b has Slope m. Topic C: Slope and Equations of Lines CFU

Concept Development Review – Ex #1 M4:LSN17 The Line Joining Two Distinct Points of the Graph y = mx + b has Slope m. Concept Development Review – Ex #1 Find at least three solutions to the equation 𝒚=𝟐𝒙, and graph the solutions as points on the coordinate plane. Connect the points to make a line. Find the slope of the line. x y CFU

Concept Development Review – Ex #2 M4:LSN17 The Line Joining Two Distinct Points of the Graph y = mx + b has Slope m. Concept Development Review – Ex #2 Find at least three solutions to the equation 𝒚=𝟑𝒙−𝟏, and graph the solutions as points on the coordinate plane. Connect the points to make a line. Find the slope of the line x y CFU

Concept Development Review – Ex #3 M4:LSN17 The Line Joining Two Distinct Points of the Graph y = mx + b has Slope m. Concept Development Review – Ex #3 Find at least three solutions to the equation 𝒚=𝟑𝒙+𝟏, and graph the solutions as points on the coordinate plane. Connect the points to make a line. Find the slope of the line. x y CFU

How can I solve for y? What is the slope? M4:LSN17 The Line Joining Two Distinct Points of the Graph y = mx + b has Slope m. Concept Development An equation in the form 𝑦=𝑚𝑥+𝑏 makes it easy to identify the slope. 𝐲=𝟐𝐱 𝐲=𝟑𝐱 −𝟏 𝐲=𝟑𝐱+𝟏 𝟖𝒙+𝟐𝒚=𝟔 How can I solve for y? 𝟖𝒙+𝟐𝒚=𝟔 −𝟖𝒙 −𝟖𝒙 𝟐𝒚=−𝟖𝒙+𝟔 What is the slope? ÷𝟐 ÷𝟐 𝒚=−𝟒𝒙+𝟑 CFU

What is the slope? Hint: Solve for y first M4:LSN17 The Line Joining Two Distinct Points of the Graph y = mx + b has Slope m. Concept Development – What is the slope? Hint: Solve for y first x + 𝒚=𝟓 −𝟐𝒙+𝒚=𝟏 CFU

Skill Development/Guided Practice – Notes #4 M4:LSN17 The Line Joining Two Distinct Points of the Graph y = mx + b has Slope m. Skill Development/Guided Practice – Notes #4 The graph of the equation 𝒚=𝟕𝒙−𝟑 has what slope? CFU

The graph of the equation 𝒚=− 𝟑 𝟒 𝒙−𝟑 has what slope? M4:LSN17 The Line Joining Two Distinct Points of the Graph y = mx + b has Slope m. Skill Development/Guided Practice– Notes #5 The graph of the equation 𝒚=− 𝟑 𝟒 𝒙−𝟑 has what slope? CFU

𝒚=𝟐𝒙+𝟐𝟎 CFU It represents how much money is saved each week. M4:LSN17 The Line Joining Two Distinct Points of the Graph y = mx + b has Slope m. Skill Development/Guided Practice– Notes #6 You have $20 in savings at the bank. Each week, you add $2 to your savings. Let 𝑦 represent the total amount of money you have saved at the end of 𝑥 weeks. Write an equation to represent this situation and identify the slope of the equation. What does that number represent? 𝒚=𝟐𝒙+𝟐𝟎 It represents how much money is saved each week. The slope is 𝟐. CFU

Skill Development/Guided Practice– Notes PS 4a M4:LSN17 The Line Joining Two Distinct Points of the Graph y = mx + b has Slope m. Skill Development/Guided Practice– Notes PS 4a Solve the following equation for 𝒚: 𝟓𝒙−𝒚=𝟒 𝟓𝒙−𝒚=𝟒 +𝒚 +𝒚 a. Based on your transformed equation, what is the slope of the linear equation 𝟓𝒙−𝒚=𝟒? 𝟓𝒙=𝒚+𝟒 −𝟒 −𝟒 𝟓𝒙−𝟒=𝒚 𝒚=𝟓𝒙−𝟒 CFU

𝒙 𝒚 CFU Skill Development/Guided Practice– Notes PS 4b M4:LSN17 The Line Joining Two Distinct Points of the Graph y = mx + b has Slope m. Skill Development/Guided Practice– Notes PS 4b Complete the table to find solutions to the linear equation. 𝒙 Transformed linear equation:  𝒚=𝟓𝒙−𝟒 𝒚 −𝟏 𝒚=𝟓 −𝟏 −𝟒 =−𝟓−𝟒 =−𝟗 −𝟗 𝟎 𝒚=𝟓 𝟎 −𝟒 =𝟎−𝟒 =−𝟒 −𝟒 𝟏 𝒚=𝟓 𝟏 −𝟒 =𝟓−𝟒 =𝟏 𝟐 𝒚=𝟓 𝟐 −𝟒 =𝟏𝟎−𝟒 =𝟔 𝟔 CFU

Skill Development/Guided Practice– Notes PS 4c M4:LSN17 The Line Joining Two Distinct Points of the Graph y = mx + b has Slope m. Skill Development/Guided Practice– Notes PS 4c Graph the points on the coordinate plane. 𝒙 𝒚 −𝟏 −𝟗 𝟎 −𝟒 𝟏 𝟐 𝟔 CFU

Find the slope between any two points. M4:LSN17 The Line Joining Two Distinct Points of the Graph y = mx + b has Slope m. Skill Development/Guided Practice– Notes PS 4d & e Find the slope between any two points. Using points (𝟎, −𝟒) and (𝟏, 𝟏): 𝒎= −𝟒−𝟏 𝟎−𝟏 𝒎= −𝟓 −𝟏 𝒎=𝟓 The slope you found in part (d) should be equal to the slope you noted in part (a). If so, connect the points to make the line that is the graph of an equation of the form 𝒚=𝒎𝒙+𝒃 that has slope 𝒎. CFU

Skill Development/Guided Practice– Notes PS 4f M4:LSN17 The Line Joining Two Distinct Points of the Graph y = mx + b has Slope m. Skill Development/Guided Practice– Notes PS 4f Note the location (ordered pair) that describes where the line intersects the 𝒚-axis. CFU

Slope – Intercept Form of a line. 𝑦=𝑚𝑥+𝑏 where 𝑚 is the slope and 𝑏 is the 𝑦 – intercept.

Closure – Solve the following equation for y: 35𝑥−7𝑦=49 What is the slope of the equation in problem 1? 3-5 at the end of your notes in complete sentences. 3. What did we learn today? 4. Why is this important to you? 5. What does the m in y = mx + b stand for? What does the b stand for? CFU