Rate of change

Front

What is the rate of change in a linear relationship?

Back

The rate of change in a linear relationship is the constant ratio of the change in the dependent variable (y) to the change in the independent variable (x), often represented as 'm' in the slope-intercept form of a line, y = mx + b.

Front

What does the constant of proportionality represent in the equation y = kx?

Back

The constant of proportionality (k) represents the factor by which the independent variable (x) is multiplied to obtain the dependent variable (y). It indicates how much y changes for a unit change in x.

Front

Write the equation for a situation where y increases by 5 for every increase of 1 in x.

Back

y = 5x.

Front

If the constant of proportionality is k = 3, what is the equation of the line?

Back

y = 3x.

Front

In the equation y = 7x, what is the rate of change?

Back

The rate of change is 7.

Front

What does a constant of proportionality of k = 10 mean in a real-world context?

Back

It means that for every unit increase in x, y increases by 10 units.

Front

How do you determine the constant of proportionality from a table of values?

Back

To determine the constant of proportionality, divide the value of y by the corresponding value of x for any pair of values in the table.

Front

If y = 12x, what is the value of y when x = 4?

Back

y = 12 * 4 = 48.

Front

What is the slope of the line represented by the equation y = 2.5x + 3?

Back

The slope (rate of change) is 2.5.

Front

If a graph shows a straight line passing through the origin, what can be said about the relationship between x and y?

Back

The relationship is directly proportional, meaning y = kx for some constant k.