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 point where the line crosses the y-axis. It is the value of y when x = 0.

Front

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

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

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.

Front

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

Back

A function is linear if the differences between consecutive y-values are constant when the x-values increase by the same amount.

Front

What does it mean for a linear function to be increasing?

Back

A linear function is increasing if the slope (m) is positive, meaning as x increases, y also increases.

Front

What does it mean for a linear function to be decreasing?

Back

A linear function is decreasing if the slope (m) is negative, meaning as x increases, y decreases.

Front

How do you graph a linear function?

Back

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

Front

What is the equation of a line with a slope of 2 and a y-intercept of -3?

Back

The equation is y = 2x - 3.