Comparing Linear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, represented by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

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

Front

How do you determine 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

If two lines have the same slope, what can we say about their steepness?

Back

If two lines have the same slope, they have the same steepness.

Front

What does it mean if a slope is negative?

Back

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

Front

What does it mean if a slope is positive?

Back

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

Front

How can you tell if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

Front

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

Back

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the significance of the y-intercept in a real-world context?

Back

The y-intercept can represent the starting value of a situation before any changes occur.