Comparing Linear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a linear function represent?

Back

The slope represents the rate of change of the function, indicating how much y changes for a unit change in x.

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the equation y = mx + b.

Front

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

Back

The rate of change can be determined by calculating the difference in y-values divided by the difference in x-values between two points.

Front

If two linear functions have the same slope, what can be said about their rates of change?

Back

If two linear functions have the same slope, they have the same rate of change.

Front

How can you compare the y-intercepts of two linear functions?

Back

You can compare the y-intercepts by looking at the constant term (b) in their equations; the larger the b, the higher the y-intercept.

Front

What does it mean if two linear functions intersect?

Back

If two linear functions intersect, it means they have at least one point in common, which represents a solution to the equations.

Front

How do you find the cost of services represented by linear functions?

Back

To find the cost, substitute the number of items (like movies) into the function's equation and calculate the resulting value.

Front

What is the significance of the coefficients in a linear function?

Back

The coefficients indicate the slope and y-intercept, which determine the steepness and position of the line on the graph.

Front

What is the formula for calculating the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).