Comparing Linear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It 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 of a linear function represents the rate of change of the function. It indicates 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. It is the value of y when x = 0.

Front

How do you find the y-intercept from the equation y = mx + b?

Back

The y-intercept is the value of b in the equation y = mx + b.

Front

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

Back

If two linear functions have the same slope, their graphs are parallel to each other.

Front

What does it mean if two linear functions have the same y-intercept?

Back

If two linear functions have the same y-intercept, their graphs intersect the y-axis at the same point.

Front

How can you determine which linear function has a greater slope?

Back

The function with the larger absolute value of the slope (m) has a greater slope.

Front

What is the significance of the slope in real-world applications?

Back

The slope can represent speed, growth rate, or any other rate of change in real-world scenarios.

Front

How do you compare the y-intercepts of two linear functions given their equations?

Back

Substitute x = 0 into both equations to find the y-intercepts and compare the resulting values.

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).