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 expresses how many units of one quantity correspond to one unit of another quantity.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, usually represented as 'm' in the equation of a line (y = mx + b). It is calculated as the change in y divided by the change in x (rise/run).

Front

What does it mean for a graph to be proportional?

Back

A graph is proportional if it passes through the origin (0,0) and has a constant rate of change, meaning the ratio of y to x is constant.

Front

What is a non-proportional relationship?

Back

A non-proportional relationship does not have a constant rate of change and does not pass through the origin. The ratio of y to x varies.

Front

How do you find the rate of change from a table of values?

Back

To find the rate of change, calculate the difference in y-values divided by the difference in x-values between two points.

Front

If y = kx represents direct variation, what does 'k' represent?

Back

In the equation y = kx, 'k' represents the constant of variation, which is the unit rate or slope of the line.

Front

What is the formula to calculate the unit rate?

Back

The unit rate can be calculated using the formula: Unit Rate = Total Quantity / Number of Units.

Front

If a car travels 150 miles in 3 hours, what is the unit rate of speed?

Back

The unit rate of speed is 50 miles per hour (150 miles / 3 hours).

Front

How do you determine if a relationship is directly proportional?

Back

A relationship is directly proportional if the ratio of y to x is constant and can be expressed as y = kx, where k is a non-zero constant.

Front

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

Back

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