Identifying the Constant of Proportionality in Tables, Graphs, and Equations

This lesson covers the concept of proportionality, focusing on how it appears in graphs, tables, and equations. It explains how to determine if a relationship is proportional by checking for a constant rate of change in graphs, consistent ratios in tables, and the form y=KX in equations. Examples are provided to illustrate these concepts, emphasizing the importance of understanding proportionality for standardized tests.

What is essential for a graph to show a proportional relationship?

• The graph should have a varying slope.

• The graph must form a straight line and pass through (0,0).

• The graph must pass through the point (1,1).

• The graph must contain a curved line.

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

• Dividing any y-value by its corresponding x-value.

• By finding the slope of the line.

• Adding all the y-values together.

• It cannot be determined from a graph.

Is a graph that forms a straight line but does not pass through (0,0) proportional?

• Yes, if it passes through (1,1).

• It depends on the slope of the line.

• No, it must also pass through (0,0).

• Yes, always.

What indicates a table shows a proportional relationship?

• All x-values are equal.

• All y-values divided by x-values give a different result.

• Each y-value divided by its corresponding x-value equals the same number.

• The table contains only positive numbers.

In a table showing a proportional relationship, what should the ratio of y to x represent?

• The y-intercept of the graph

• The constant of proportionality

• The slope of the graph

• The x-intercept of the graph

Can a table with varying ratios of y to x be proportional?

• Yes, if the differences are minor.

• Yes, but only in special cases.

• No, unless all x-values are the same.

• No, the ratios must be consistent.

Which equation form indicates a proportional relationship?

• y = k - x

• y = x + k

• y = kx

• y = k/x

What is the constant of proportionality in the equation y = -8.9x?

• -8.9

• 8.9

• 0

• -1

If an equation is in the form y = 5x + 3, is it proportional?

• Yes, if x is always positive.

• Yes, because it has a y and x.

• No, because it does not include a division by x.

• No, because it includes an additional constant.

What does a constant of proportionality of 12 indicate in a graph?

• The total area under the graph is 12.

• For every increase in x by 1, y increases by 12.

• The graph passes through the point (12,12).

• The graph is a circle with radius 12.