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 quantity of one. For example, if a car travels 300 miles in 5 hours, the unit rate is 60 miles per hour.

Front

How do you find the slope of a line given two points?

Back

The slope (m) of a line can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, meaning the line is decreasing from left to right.

Front

What is the constant of proportionality?

Back

The constant of proportionality is the constant value (k) that relates two proportional quantities, often represented in the equation y = kx.

Front

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

Back

A relationship is proportional if the ratio of y to x is constant for all pairs of values in the table.

Front

What is the formula for calculating the rate of change?

Back

The rate of change can be calculated using the formula: Rate of Change = (Change in y) / (Change in x).

Front

If a job pays $14 per hour, how much will be earned for 10 hours of work?

Back

To find the total earnings, multiply the hourly rate by the number of hours: $14/hour * 10 hours = $140.

Front

What is the relationship between slope and rate of change?

Back

The slope of a line represents the rate of change between the two variables; it indicates how much y changes for a unit change in x.

Front

How do you write an equation for a proportional relationship?

Back

An equation for a proportional relationship can be written in the form y = kx, where k is the constant of proportionality.

Front

What does it mean for two quantities to be directly proportional?

Back

Two quantities are directly proportional if they increase or decrease at the same rate, meaning their ratio remains constant.