Algebra 1 Name: ________________________________________ Date: _________________________________________ Class#: ________________________________________

5.1 Guided Notes Intro to Slope

What is slope? ________________________________________________________________

Increasing   Decreasing   Zero   Undefined  

m=___________   m=___________   m=___________   m=___________  

 

 

 

 

 

 

 

 

Relationship to Family of Functions With family of functions, we said that linear functions were of the form y = ax + k. Now, we will be using the format y = mx + b. How do they relate? _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________

Recall

If |a| < 1 à_____________________ If |a| = 1 à_____________________ If |a| > 1 à_____________________

If |m| < 1 à_____________________ If |m| = 1 à_____________________ If |m| > 1 à_____________________

Finding the Slope of a Line Given Two Points The slope of the nonvertical line passing through the points (x1, y1) and (x2, y2) is:

2 1

2 1

y y risemx x run−= =−

Example 1: Find the slope of the line passing through ( 2,0)− and (1,2) .

2 1

2 1

y ymx x

−=− =

−−

Example 2: Find the slope of the line that passes through the points (-5, 9) and (-4, -3) Example 3: Without graphing, tell which line is steeper.

Line 1: through (- 1, 0) and (0, 5) Line 2: through (2, 4) and (3, 7)

You Try! 1. Find the slope of the line passing through the given points. Label it as increasing, decreasing,

horizontal, or vertical.

a. (2, - 4) and (- 5, 1).

b. (-8, 3) and (2, 11).

Increasing Decreasing Horizontal Vertical Increasing Decreasing Horizontal Vertical

c. (5, - 3) and ( 5, 2)

d. (0, - 2) and (- 6, -2).

Increasing Decreasing Horizontal Vertical Increasing Decreasing Horizontal Vertical

2. Without graphing, tell whether the line through (0, 3) and (5, - 5) rises, falls, is horizontal, or is

vertical. Explain your reasoning.

3. Which line is steeper? Explain your answer by showing your work and making a statement about what your work proves.

Line 1: through (- 5, 1) and (0, 3) Line 2: through (0, 7) and (3, 9)

Line ___________________ is steeper. I know this because: ________________________________

_________________________________________________________________________________

Finding the Slope of a Line Given a Graph

m = rise

run= ↔

Example 1: Positive Slope

Example 2: Negative Slope

You Try! Find the slope using the graph.

1.

2.

3.

4.

Finding the Slope of a Line Given a Table A table is a very useful tool because it helps you to identify a pattern. A table can help you to determine if a given data set is in fact linear. If it is linear, then we can proceed to find the slope of the linear relationship. There are two methods to finding the slope of a linear relationship from a table. Method 1: Identify the pattern

Method 2: Use the slope formula You Try! 1. Find the slope using the table given below.

a. Identify the pattern b. Use the slope formula.

x y -2 -8 -1 -3 0 2 1 7 2 12

x y -2 -8 -1 -3 0 2 1 7 2 12

x y -4 0 -2 -4 0 -8 2 -12 4 -16

x y -2 -8 -1 -3 0 2 1 7 2 12

Finding the Slope of a Line Given a Word Problem Identifying the Slope The cost of a school banquet is $95 plus an additional $15 for each person attending.

a. What is the rate of the pricing?

b. Explain what the slope means. For every additional ________________<x>, the __________________<y> increases/decreases by __________________<m>.

Calculating the Slope from a Word Problem In 1970, there were 160 African American women in elected public office in the United States. By 1993, the number had increased to 2332. Find the average rate of change for the number of African American women who held office at any given time between 1970 & 1993.

a. Identify your variables:

Independent Variable (x) :_____________

Dependent Variable(y):________________

b. What is (x1, y1) and (x2, y2)?

(x1, y1)__________________ (x2, y2)__________________

c. Calculate the slope using the formula.

d. Explain what the slope means.

For every additional ________________<x>, the __________________<y> increases/decreases by __________________<m>.

You Try! 1. A company offers you a salary of $2,000 per month plus a signing bonus of $10,000. What is the yearly salary rate? 2. Jamal’s parents give him $20 to spend at camp. Jamal spends the same amount of money on snacks each day. After 4 days he has $12 left. What rate is Jamal spending money?

a. Calculate the slope using the formula.

b. Explain what the slope means.

Challenge! The roof of a house rises 5 feet over a horizontal distance of 15 feet.

a. Find the slope of the roof.

b. If the roof was rebuilt with a slope of 2

5 and still has a horizontal distance of 15 feet, what is the

rise of the roof?