Compare 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 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 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 two points on the line.

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 does it mean if one linear function has a greater slope than another?

Back

If one linear function has a greater slope than another, it rises more steeply than the other function as x increases.

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 tell if a linear function is increasing or decreasing?

Back

A linear function is increasing if its slope is positive (m > 0) and decreasing if its slope is negative (m < 0).

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

What is the difference between a positive slope and a negative slope?

Back

A positive slope indicates that as x increases, y also increases, while a negative slope indicates that as x increases, y decreases.

Front

How do you graph a linear function?

Back

To graph a linear function, you can plot the y-intercept on the y-axis and use the slope to find another point. Then, draw a straight line through the points.