Constructing 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 (m) represent in a linear function?

Back

The slope (m) 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 (b) in a linear function?

Back

The y-intercept (b) is the value of y when x is 0. It is the point where the line crosses the y-axis.

Front

How do you find the rate of change from a linear function?

Back

The rate of change can be found by calculating the slope (m) of the line, which is the change in y divided by the change in x.

Front

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

Back

The formula for slope is m = (y2 - y1) / (x2 - x1).

Front

If a linear function has a slope of -2, what does this indicate about the function?

Back

A slope of -2 indicates that for every 1 unit increase in x, y decreases by 2 units.

Front

What is the initial value of a linear function?

Back

The initial value is the y-intercept (b) of the function, representing the starting point of the function on the y-axis.

Front

How can you represent a real-world situation with a linear function?

Back

You can represent a real-world situation by identifying the variables involved, determining the rate of change, and finding the initial value.

Front

What does it mean if a linear function has a positive slope?

Back

A positive slope means that as x increases, y also increases, indicating a direct relationship between the two variables.

Front

What does it mean if a linear function has a negative slope?

Back

A negative slope means that as x increases, y decreases, indicating an inverse relationship between the two variables.