Proportional Relationships and Equations

Front

What is a proportional relationship?

Back

A proportional relationship is a relationship between two quantities where the ratio of one quantity to the other quantity is constant.

Front

How can you determine if a relationship is proportional using a table of values?

Back

A relationship is proportional if the ratios of corresponding values are equal for all pairs of values in the table.

Front

What does the equation y = kx represent in a proportional relationship?

Back

In the equation y = kx, 'k' is the constant of proportionality, which represents the ratio of y to x.

Front

If 10 concrete blocks weigh 100 pounds, how much do 15 concrete blocks weigh?

Back

15 concrete blocks would weigh 150 pounds, as the weight is proportional to the number of blocks.

Front

What is the constant of proportionality in the equation y = 1/2x?

Back

The constant of proportionality is 1/2, meaning for every 1 meal, the cost is half a dollar.

Front

How do you solve for x in the equation y = 3/2x when y = 12?

Back

To solve for x, set y to 12: 12 = 3/2x. Multiply both sides by 2/3 to get x = 8.

Front

What is the meaning of the slope in a proportional relationship?

Back

The slope represents the rate of change between the two quantities, indicating how much one quantity changes in relation to the other.

Front

How can you identify a non-proportional relationship?

Back

A non-proportional relationship can be identified if the ratios of corresponding values are not constant or if the graph does not pass through the origin.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x is 0, indicating where the line crosses the y-axis.

Front

In the equation y = mx + b, what do 'm' and 'b' represent?

Back

In the equation, 'm' represents the slope of the line, and 'b' represents the y-intercept.