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 (upward or downward).

Front

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

Back

To find the y-intercept, set x = 0 in the equation and solve for y. The y-intercept is the point where the line crosses the y-axis.

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 does a positive slope indicate about a linear function?

Back

A positive slope indicates that as x increases, y also increases, meaning the line rises from left to right.

Front

What does a negative slope indicate about a linear function?

Back

A negative slope indicates that as x increases, y decreases, meaning the line falls from left to right.

Front

What is the y-intercept in the equation y = 3x + 2?

Back

The y-intercept is 2, which means the line crosses the y-axis at the point (0, 2).

Front

How can you determine if a line is horizontal or vertical?

Back

A horizontal line has a slope of 0 and can be expressed as y = b. A vertical line has an undefined slope and can be expressed as x = a.

Front

What is the significance of the point (0, b) in a linear function?

Back

The point (0, b) represents the y-intercept of the linear function, where the line crosses the y-axis.

Front

How do you graph a linear function?

Back

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