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 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 in 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

If the slope of a line is negative, what does that indicate about the line's direction?

Back

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

Front

What is the independent variable in a linear function?

Back

The independent variable is the variable that represents the input of the function, often denoted as x.

Front

What is the dependent variable in a linear function?

Back

The dependent variable is the variable that represents the output of the function, often denoted as y.

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 divided by the differences between consecutive x-values are constant.

Front

What does the equation y = -x + 2 represent graphically?

Back

This equation represents a straight line with a slope of -1 and a y-intercept of 2.

Front

What is the formula for the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.