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 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?

Back

The y-intercept is the point where the graph of a function crosses the y-axis. It is represented by the value of b in the equation y = mx + b.

Front

What is the x-intercept?

Back

The x-intercept is the point where the graph of a function crosses the x-axis. It is found by setting y to 0 and solving for x.

Front

How do you find the slope from two points?

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 is the equation of a line with a slope of 5 and a y-intercept of 2?

Back

The equation is y = 5x + 2.

Front

What does a positive slope indicate about a linear function?

Back

A positive slope indicates that as x increases, y also increases, showing a direct relationship.

Front

What does a negative slope indicate about a linear function?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship.

Front

What is the rate of change in a linear function?

Back

The rate of change is the same as the slope of the line, representing how much y changes for a unit change in x.

Front

How can you determine if a function is linear from a table of values?

Back

If the differences between consecutive y-values divided by the differences between consecutive x-values are constant, the function is linear.