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 represents the rate of change of the function. It indicates how much y changes for a unit change in x.

Front

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

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

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 can you determine which of two linear functions has a greater slope?

Back

Compare the coefficients of x (the slopes) in their equations. The function with the larger coefficient has the greater slope.

Front

What does it mean if two linear functions have the same slope?

Back

If two linear functions have the same slope, they are parallel and will never intersect.

Front

What is the significance of the initial fee in a linear cost function?

Back

The initial fee is the fixed cost that does not change with the number of units (e.g., guests) and is represented by the y-intercept in the cost equation.

Front

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

Back

The slope can represent a rate, such as cost per hour or guests per dollar, indicating how one quantity changes in relation to another.

Front

What is the formula for a linear equation in slope-intercept form?

Back

The formula is y = mx + b, where m is the slope and b is the y-intercept.

Front

How can you find the y-intercept from a linear equation?

Back

To find the y-intercept, set x = 0 in the equation and solve for y.