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 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 determine which linear function has a greater y-intercept?

Back

To determine which linear function has a greater y-intercept, compare the constant term (b) in the equation y = mx + b for each function.

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 and will never intersect.

Front

What is the significance of the rate of change in linear functions?

Back

The rate of change indicates how steep the line is. A higher rate of change means the line rises or falls more steeply.

Front

How can 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 the coordinates of the two points.

Front

What does it mean if two linear functions intersect?

Back

If two linear functions intersect, it means they have a common solution, or point, where both functions have the same value of y for the same value of x.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By + C = 0, where A, B, and C are constants.

Front

How do you convert a linear equation from slope-intercept form to standard form?

Back

To convert from slope-intercept form (y = mx + b) to standard form (Ax + By = C), rearrange the equation to get all terms on one side.