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 line represent?

Back

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

Front

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is 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

What is 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 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

How can you determine if a point lies on a linear function?

Back

To determine if a point (x, y) lies on a linear function, substitute x into the function's equation and check if the resulting y equals the y-coordinate of the point.

Front

What is a T-Table in relation to linear functions?

Back

A T-Table is a tool used to organize values of x and their corresponding y values for a linear function, helping to visualize the relationship.

Front

What is the significance of the equation y = 4/3x + 4?

Back

This equation represents a linear function with a slope of 4/3 and a y-intercept of 4.