Understanding Slope and Linear Relationships

This lesson introduces non-proportional linear relationships, using examples like the stacking cups problem and Andre's babysitting earnings. It explains how to determine the rate of change using slope triangles and how to write equations from these relationships. The lesson emphasizes understanding the difference between proportional and non-proportional relationships and provides a foundation for writing equations based on slope and intercepts.

What distinguishes a non-proportional linear relationship from a proportional one?

• The rate of change is variable.

• The relationship is non-linear.

• The starting point is not zero.

• The graph is a curve.

In the babysitting example, what does the $15 per hour represent?

• The maximum amount Andre can earn.

• The rate of change or slope.

• The initial payment for starting the job.

• The total earnings after 10 hours.

Why does Andre receive $10 before starting his babysitting job?

• As a bonus for good performance.

• To encourage him to work more hours.

• To cover travel expenses to the job.

• As a penalty for late arrival.

How do you calculate the slope using a slope triangle?

• By adding the vertical and horizontal changes.

• By dividing the vertical change by the horizontal change.

• By subtracting the horizontal change from the vertical change.

• By dividing the horizontal change by the vertical change.

What is the slope if Andre works 4 more hours and earns $60?

• $25 per hour

• $20 per hour

• $10 per hour

• $15 per hour

What is the purpose of sliding the slope triangle in the graph?

• To align it with the origin for easier calculation.

• To change the slope value.

• To increase the number of units in the vertical direction.

• To decrease the number of units in the horizontal direction.

How is the equation y - 40 = 15(x - 2) derived?

• By multiplying the slope by the x-coordinate.

• By adding the initial payment to the total earnings.

• By subtracting the initial payment from the total earnings.

• By equating the vertical and horizontal changes to the slope.

What does the term 'x - 8' represent in the equation y - 130 = 15(x - 8)?

• The total earnings after 8 hours.

• The initial payment received.

• The number of hours after subtracting the initial hours.

• The total number of hours worked.

Why is it important to understand the starting point in these equations?

• It is crucial for calculating the total hours worked.

• It affects the slope of the line.

• It influences the initial payment and overall equation.

• It determines the maximum earnings possible.

What remains consistent across different slope triangles and equations?

• The total earnings after 10 hours.

• The slope or rate of change.

• The total number of hours worked.

• The initial payment amount.