Unit 3 - Proportional Relationships (Pre-Algebra)

Unit 3 - Proportional Relationships (Pre-Algebra)

Ms. Brower

2020-2021

Types of Slope

• Positive

• Negative

• Zero

• Undefined

Positive Slope

• Increases as the graph moves from left to right.

Negative Slope

• Decreases as the graph moves from left to right.

Zero Slope

• Does not move up or down.

• Horizontal line from left to right.

• This happens when there is a ZERO in the NUMERATOR.

• This happens when both "y" values are the same.

Undefined Slope

• Vertical line up and down.

• This happens when there is a ZERO in the DENOMINATOR.

• This happens when both "x" values are the same.

Multiple Choice

Which graph shows a positive slope?

Multiple Choice

Which graph shows a zero slope?

Multiple Choice

Which graph shows a negative slope?

Multiple Choice

Which graph shows an undefined slope?

Poll

True or False: An Undefined Slope is a Vertical Line.

• FALSE

• TRUE

Poll

True or False: A Zero Slope is a Horizontal Line.

• TRUE

• FALSE

Finding the Slope Using the Slope Formula

•  $\left(x_1,\ y_1\right)\ and\ \left(x_2,\ y_2\right)$  

•  $slope=m=\frac{y_2-y_1\text{y}}{x_2-x_1}$  

Multiple Choice

Find the slope of the line through the points

 $\left(0,\ 8\right)\ and\ \left(-2,1\right)$  

•  $\frac{7}{2}$  

•  $\frac{-7}{2}$  

•  $\frac{2}{7}$  

• ZERO

• UNDEFINED

Multiple Choice

Find the slope of the line through the points

 $\left(-4,\ 8\right)\ and\ \left(-4,\ 3\right)$  

•  $\frac{8}{5}$  

• ZERO

• UNDEFINED

•  $\frac{5}{8}$  

Multiple Choice

Find the slope of the line through the points

 $\left(-4,\ -2\right)\ and\ \left(5,\ -2\right)$  

• ZERO

• UNDEFINED

•  $\frac{9}{1}$  

•  $\frac{1}{4}$  

Multiple Choice

Find the slope of the line through the points

 $\left(-5,\ 3\right)\ and\ \left(-7,\ 4\right)$  

• UNDEFINED

• ZERO

•  $\frac{-1}{2}$  

•  $-2$  

Proportional Relationships

• Equations of proportional relationships are in the form:   $y=mx$ , where represents the slope (unit rate, constant of proportionality, rate of change). 

• Graphs of proportional relationships begin at the origin and are straight diagonal lines. 

• A table represents a proportional relationship if all values of  $\frac{y}{x}$  are the same. 

Poll

True or False: The graph of a proportional relationship can be a curved line.

• TRUE

• FALSE

Poll

True or False: The graph of a proportional relationship must begin at the origin.

• TRUE

• FALSE

Identifying Functions

• A relation is a function if there are NO REPEATS in the DOMAIN.

• The DOMAIN is also referred to as the INPUT or the X-VALUES.

• The RANGE is also referred to as the OUTPUT or the Y-VALUES.

• Functions can be represented as a set of ordered pairs, in tables, in graphs, in equations, and in mapping diagrams.

Multiple Choice

Is it a function?

• YES

• NO

Multiple Choice

Is it a function?

• YES

• NO

Multiple Choice

Is it a function?

• YES

• NO

Multiple Choice

Is it a function?

• YES

• NO

Multiple Choice

Is it a function?

• YES

• NO

Multiple Choice

Is it a function?

• YES

• NO