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 y-value with respect to the x-value. It indicates how steep the line is.

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 y-intercept in the equation of a line?

Back

The y-intercept is the point where the line crosses the y-axis. In the equation y = mx + b, b represents the y-intercept.

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.

Front

How do you determine if a function is linear?

Back

A function is linear if it can be expressed in the form y = mx + b, where m and b are constants.

Front

What is the slope of the line represented by the equation y = -3x + 2?

Back

The slope of the line is -3.

Front

If a line has a slope of 1/2, what does this mean?

Back

A slope of 1/2 means that for every 2 units you move horizontally to the right, the line rises 1 unit vertically.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.