Comparing Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has 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

What is the y-intercept in a linear function?

Back

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

Front

How do you determine 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 about a linear function?

Back

A positive slope indicates that as x increases, y also increases, meaning the line rises from left to right.

Front

What does a negative slope indicate about a linear function?

Back

A negative slope indicates that as x increases, y decreases, meaning the line falls from left to right.

Front

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

Back

The initial fee is the fixed cost that must be paid regardless of the number of units (e.g., guests, visits) and is represented by the y-intercept in the equation.

Front

How can you compare the steepness of two linear functions?

Back

You can compare the steepness by looking at the absolute values of their slopes. The function with the larger absolute slope is steeper.

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, indicating they have the same rate of change.

Front

What is the formula for a linear function?

Back

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