Linear Functions

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 y with respect to x. It indicates how steep the line is and the direction it goes (positive or negative).

Front

How do you find the y-intercept of a linear function?

Back

The y-intercept is found by setting x = 0 in the equation of the linear function and solving for y.

Front

What is the formula for calculating 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 the function y = -2x + 5?

Back

The y-intercept is 5, which is the value of y when x = 0.

Front

If a line has a slope of 4, what does this mean?

Back

A slope of 4 means that for every 1 unit increase in x, y increases by 4 units.

Front

What is the slope of the line represented by the equation y = 3x - 1?

Back

The slope of the line is 3.

Front

How do you determine if a slope is positive or negative?

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 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.