Linear Functions in Context

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, represented by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the dependent variable with respect to the independent variable.

Front

How do you interpret the slope in a real-world context?

Back

In a real-world context, the slope indicates how much one quantity changes for a unit change in another quantity.

Front

What is the y-intercept in a linear function?

Back

The y-intercept is the value of y when x is 0, representing the starting point of the function on the y-axis.

Front

What does f(1990)=214 mean in a linear function context?

Back

It means that in the year 1990, the value of the function (e.g., number of people with health insurance) was 214.

Front

How can you find the slope from two points on a line?

Back

The slope (m) 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 positive slope indicate?

Back

A positive slope indicates that as the independent variable increases, the dependent variable also increases.

Front

What does a negative slope indicate?

Back

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

Front

What is the significance of a slope of zero?

Back

A slope of zero indicates a horizontal line, meaning there is no change in the dependent variable as the independent variable changes.

Front

What does it mean if a line is vertical?

Back

A vertical line has an undefined slope, indicating that the independent variable does not change while the dependent variable can take any value.