Unit rate/slope/ rate of change

Front

What is a unit rate?

Back

A unit rate is a comparison of two different quantities where one of the quantities is expressed as a single unit. For example, if you earn $100 for 2 hours of work, the unit rate is $50 per hour.

Front

How do you calculate the slope of a line?

Back

The slope of a line is calculated by taking the difference in the y-coordinates and dividing it by the difference in the x-coordinates of two points on the line. Formula: slope (m) = (y2 - y1) / (x2 - x1).

Front

What does a negative slope indicate?

Back

A negative slope indicates that as one variable increases, the other variable decreases. This shows an inverse relationship between the two variables.

Front

What is the constant of proportionality?

Back

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

Front

If y = 39 when x = 3, what is the constant of proportionality?

Back

The constant of proportionality k = y/x = 39/3 = 13.

Front

What is the rate of change?

Back

The rate of change describes how much one quantity changes in relation to another quantity. It is often represented as the slope of a line.

Front

How do you find the rate of change from two points (x1, y1) and (x2, y2)?

Back

Rate of change = (y2 - y1) / (x2 - x1).

Front

What does a slope of 0 mean?

Back

A slope of 0 means that the line is horizontal, indicating that there is no change in the y-value as the x-value changes.

Front

What is direct variation?

Back

Direct variation is a relationship between two variables where one variable is a constant multiple of the other. It can be expressed as y = kx.

Front

If the rate of change is -2 gallons per minute, what does this mean?

Back

This means that for every minute that passes, the quantity decreases by 2 gallons.