Rate of Change of Linear Functions Warmup 4

Front

What is the rate of change in a linear function?

Back

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

Front

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

Back

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

Front

What does a positive rate of change indicate about a linear function?

Back

A positive rate of change indicates that as the independent variable increases, the dependent variable also increases, resulting in an upward slope.

Front

What does a negative rate of change indicate about a linear function?

Back

A negative rate of change indicates that as the independent variable increases, the dependent variable decreases, resulting in a downward slope.

Front

What is the rate of change if the line goes through the points (1, 2) and (3, 6)?

Back

Rate of change = (6 - 2) / (3 - 1) = 4 / 2 = 2.

Front

If a line has a rate of change of -3, what does this mean in a real-world context?

Back

It means that for every unit increase in the independent variable, the dependent variable decreases by 3 units.

Front

What is the slope of a line that rises 5 units for every 2 units it runs?

Back

The slope (rate of change) is 5/2.

Front

How can you interpret a rate of change of 0?

Back

A rate of change of 0 indicates that the dependent variable does not change as the independent variable changes, resulting in a horizontal line.

Front

What is the formula for the slope of a line in slope-intercept form?

Back

The formula is y = mx + b, where m is the slope (rate of change) and b is the y-intercept.

Front

If a ticket price increases from $10 to $15 over 5 weeks, what is the rate of change?

Back

Rate of change = (15 - 10) / 5 = 5 / 5 = 1 dollar per week.