1. 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

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

3. 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

4. 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

5. 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
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6. 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

7. 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

8. 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

9. 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?
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10. 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

11. 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

12. 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
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13. 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
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14. 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
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15. 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

16. 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

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

18. 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