Linear Functions - Review

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in 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 between 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 of a linear function?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of b in the equation y = mx + b.

Front

What is the difference between positive and negative slope?

Back

A positive slope means the line rises as it moves from left to right, while a negative slope means the line falls as it moves from left to right.

Front

What does a slope of zero indicate?

Back

A slope of zero indicates a horizontal line, meaning there is no change in the y-value as the x-value changes.

Front

What does an undefined slope indicate?

Back

An undefined slope indicates a vertical line, where the x-value does not change, leading to division by zero in the slope formula.

Front

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

Back

A function is linear if the rate of change (slope) between any two points is constant.

Front

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

Back

The equation is y = 3x + 2.

Front

How do you graph a linear function?

Back

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