Unit rate/slope/ rate of change

Front

What is a unit rate?

Back

A unit rate is a comparison of two different quantities when they are combined together. It is expressed as a ratio with a denominator of 1.

Front

How do you calculate the rate of change?

Back

The rate of change is calculated by taking the difference in the y-values and dividing it by the difference in the x-values (slope formula: (y2 - y1) / (x2 - x1)).

Front

What does a negative rate of change indicate?

Back

A negative rate of change indicates that as one quantity increases, the other quantity decreases.

Front

What is the constant of proportionality?

Back

The constant of proportionality is the constant value of the ratio of two proportional quantities, often represented as k in the equation y = kx.

Front

If the rate of change is 6, what does this mean in a real-world context?

Back

A rate of change of 6 means that for every unit increase in the independent variable, the dependent variable increases by 6 units.

Front

What does it mean for a relationship to be proportional?

Back

A relationship is proportional if the ratio between the two quantities remains constant.

Front

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

Back

A table of values is proportional if the ratios of corresponding y-values to x-values are the same for all pairs.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise over run (change in y over change in x).

Front

Calculate the rate of change between the points (4,5) and (2,15).

Back

The rate of change is -5.

Front

What is the slope of the line represented by the equation y = 3x + 2?

Back

The slope of the line is 3.