Understanding Slope and Proportionality

The video tutorial covers the concept of proportional relationships, focusing on how to write equations from graphs and use them to calculate values. It explains the constant of proportionality and demonstrates calculations in both directions. The tutorial includes a practical problem involving raffle tickets to illustrate these concepts. It also discusses how to determine the slope of a line and differentiate between proportional and non-proportional relationships.

What is the first step in writing an equation from a graph of a proportional relationship?

• Calculate the y-intercept

• Find where the line intersects the grid lines

• Determine the x-intercept

• Identify the slope of the line

What is the equation of a line if the constant of proportionality is 1.5?

• y = x - 1.5

• y = 1.5 + x

• y = x + 1.5

• y = 1.5x

How do you calculate the constant of proportionality from a graph?

• Multiply the x-coordinate by the y-coordinate

• Subtract the x-coordinate from the y-coordinate

• Add the x-coordinate to the y-coordinate

• Divide the y-coordinate by the x-coordinate

If you have 1000 grams of fish, how many calories are needed if the constant of proportionality is 1.5?

• 500 calories

• 1500 calories

• 1000 calories

• 2000 calories

If you sell 10 raffle tickets and make $24, what is the constant of proportionality?

• $10.00

• $0.24

• $24.00

• $2.40

What does a slope of one indicate about the relationship between the vertical and horizontal directions?

• The vertical direction is half the horizontal direction

• The vertical direction is twice the horizontal direction

• The vertical and horizontal directions are equal

• The vertical direction is one-tenth the horizontal direction

How do you determine the slope of a line when the scales on the axes are different?

• By adjusting the scales to match

• By comparing the units directly

• By ignoring the scales

• By ensuring the scales are the same

How can you identify a non-proportional relationship from an equation?

• The slope is greater than one

• The graph passes through the origin

• The equation includes a constant term

• The equation is in the form y = kx

What is the slope of a line if the vertical direction is 3 units and the horizontal direction is 11 units?

• 11/3

• 1

• 1/3

• 3/11

What happens to the y-coordinate if you double the x-coordinate in a non-proportional relationship?

• The y-coordinate does not double

• The y-coordinate doubles

• The y-coordinate remains the same

• The y-coordinate is halved