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 of a linear function represents the rate of change of the function. It indicates how much the y-value changes for a one-unit increase in the x-value.

Front

How do 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 two points on the line.

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 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 to each other and will never intersect.

Front

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

Back

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

Front

How do you interpret the graph of a linear function?

Back

The graph of a linear function shows the relationship between the independent variable (x) and the dependent variable (y). The slope indicates the direction and steepness of the line.

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.

Front

How can you identify the greater y-intercept between two linear equations?

Back

Compare the constant term (b) in the equations. The equation with the larger constant has the greater y-intercept.