Understanding Proportional Relationships

The video tutorial explores the differences between proportional and non-proportional relationships, focusing on how to analyze these relationships using graphs and slope calculations. It covers translating lines, recalculating slopes, and solving problems using fractions and decimals. The tutorial emphasizes the importance of understanding the constant of proportionality and its role in proportional relationships, while also highlighting the differences in non-proportional relationships.

What is the main difference between proportional and non-proportional relationships?

• Proportional relationships do not pass through the origin.

• Proportional relationships have a constant rate of change.

• Non-proportional relationships have a constant rate of change.

• Non-proportional relationships pass through the origin.

How can you identify a proportional relationship on a graph?

• The line is curved.

• The line passes through the origin.

• The line has a negative slope.

• The line is horizontal.

What happens to the y-intercept when a line is translated upwards?

• It increases.

• It remains the same.

• It becomes negative.

• It decreases.

When recalculating the slope after translating a line, what is the new y-intercept if the line is moved up by three halves?

• One

• Zero

• Three halves

• Two

How do you calculate the change in y compared to the change in x?

• By multiplying the y and x values.

• By dividing the change in y by the change in x.

• By subtracting the x value from the y value.

• By adding the y and x values.

What is the result of dividing 10 fourths by 5 fourths?

• 3

• 4

• 2

• 1

What is the slope of a line if the vertical change is two and a half and the horizontal change is one and one-fourth?

• 1

• 4

• 3

• 2

In a proportional relationship, how does the slope compare to the constant of proportionality?

• The slope is always less.

• They are different.

• The slope is always greater.

• They are the same.

Why can't you simply divide the y-coordinate by the x-coordinate in a non-proportional relationship?

• Because the line is curved.

• Because the y-coordinate is always zero.

• Because the line does not pass through the origin.

• Because the x-coordinate is always zero.

What must be true for a relationship to be considered proportional?

• The line must pass through the origin.

• The line must be vertical.

• The line must have a negative slope.

• The line must be horizontal.