Problem Solving Proportional Relationships

Tell whether x and y are in a proportional relationship. Explain your reasoning.

• no, the graph of the equation

  does not pass through the

  origin.

• yes, the graph

  is a line through

  the origin.

Tell whether x and y are in a proportional relationship. Explain your reasoning. If so, write an equation that represents the relationship.

Mathematical Equivalence

ON

Tell whether x and y are in a proportional relationship. Explain your reasoning. If so, write an equation that represents the relationship.

• no, the rate of change is not constant

• yes, the rate of change is constant.

The cost y (in dollars) to rent a kayak is proportional to the number x of hours that you rent the kayak. It costs $27 to rent the kayak for 3 hours.

c. How much does it cost to rent the kayak for 5 hours?

$_____

Mathematical Equivalence

ON

TICKETS: The amount y (in dollars) that you raise by selling x fundraiser tickets is represented by the equation y=5x. Graph the equation and interpret the slope.

Interpret the slope: each ticket costs $_____

Mathematical Equivalence

ON

The cost y (in dollars) to rent a kayak is proportional to the number x of hours that you rent the kayak. It costs $27 to rent the kayak for 3 hours.

a. Write an equation that represents the situation.

Mathematical Equivalence

ON

The cost y (in dollars) to rent a kayak is proportional to the number x of hours that you rent the kayak. It costs $27 to rent the kayak for 3 hours.

b. Interpret the slope.

It costs $_____ per hour to rent a kayak.

Mathematical Equivalence

ON

Problem #12a

PROBLEM SOLVING: The graph relates the temperature change y (in degrees Fahrenheit) to the altitude change x (in thousands of feet).

a. Is the relationship proportional?

• yes

• no

Problem #12a

PROBLEM SOLVING: The graph relates the temperature change y (in degrees Fahrenheit) to the altitude change x (in thousands of feet).

a. Is the relationship proportional? Explain.

• The line does not pass through the origin.

• The line does pass through the origin.

Problem #12b

PROBLEM SOLVING: The graph relates the temperature change y (in degrees Fahrenheit) to the altitude change x (in thousands of feet).

b. Interpret the slope.

• The temperature decreases by 3.5°F for each 1000-foot increase in altitude.

• The temperature increases by 3.5°F for each 1000-foot increase in altitude.