8th Flashcard: Rate of Change and Initial Value

Front

What is another name for the initial value in a linear function?

Back

y-intercept

Front

How do you calculate the rate of change in a linear function?

Back

The rate of change is calculated by finding the difference in the y-values divided by the difference in the x-values (rise over run).

Front

What does the slope of a line represent in a real-world context?

Back

The slope represents the rate of change, indicating how much the dependent variable changes for a unit change in the independent variable.

Front

In the equation y = mx + b, what does 'm' represent?

Back

'm' represents the slope of the line, which is the rate of change.

Front

In the equation y = mx + b, what does 'b' represent?

Back

'b' represents the y-intercept, which is the initial value when x = 0.

Front

If a line has a slope of 6, what is the rate of change?

Back

The rate of change is 6 units of y for every 1 unit of x.

Front

What is the rate of change for the function y = 4x - 5?

Back

The rate of change is 4.

Front

How can you interpret a negative slope in a real-world scenario?

Back

A negative slope indicates that as the independent variable increases, the dependent variable decreases.

Front

What is the significance of the y-intercept in a graph?

Back

The y-intercept indicates the starting value of the dependent variable when the independent variable is zero.

Front

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

Back

Calculate the change in y divided by the change in x for two points in the table.