Linear Functions

Front

What is the definition of a linear function?

Back

A linear function is a function that can be graphically represented in the Cartesian plane as a straight line, defined by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you calculate the slope (m) of a linear function?

Back

The slope (m) of a linear function is calculated as the change in y divided by the change in x (rise over run) between two points on the line.

Front

What does a positive slope indicate about a linear function?

Back

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

Front

What does a negative slope indicate about a linear function?

Back

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

Front

What is the y-intercept in the equation 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

How can you determine if a linear function is increasing or decreasing?

Back

A linear function is increasing if the slope (m) is positive and decreasing if the slope (m) is negative.

Front

What is the formula to find the slope between two points (x1, y1) and (x2, y2)?

Back

The formula to find the slope (m) between two points is m = (y2 - y1) / (x2 - x1).

Front

What is the significance of the slope in real-world applications?

Back

The slope represents the rate of change in real-world applications, such as speed, cost per item, or growth rate.

Front

How do you find the value of y for a given x in a linear function?

Back

To find the value of y for a given x, substitute the x value into the linear equation y = mx + b and solve for y.

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.