Linear Relationships

Front

What is a linear relationship?

Back

A linear relationship is a relationship between two variables that can be represented by a straight line on a graph. It can be described by the equation of a line, typically in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the slope of a line?

Back

The slope of a line measures the steepness and direction of the line. It is calculated as the change in y divided by the change in x (rise over run). A positive slope indicates the line rises from left to right, while a negative slope indicates it falls.

Front

What is the y-intercept?

Back

The y-intercept is the point where a line crosses the y-axis. It is represented by the value of y when x is 0 in the equation of the line.

Front

What does a positive slope indicate?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, showing a direct relationship between the two variables.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, showing an inverse relationship between the two variables.

Front

What is an undefined slope?

Back

An undefined slope occurs in a vertical line where the change in x is zero, making the slope calculation (rise/run) impossible.

Front

What is the equation of a line in slope-intercept form?

Back

The equation of a line in slope-intercept form is written as y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the slope from a table of values?

Back

To find the slope from a table of values, select two points (x1, y1) and (x2, y2) and use the formula m = (y2 - y1) / (x2 - x1).

Front

What is the x-intercept?

Back

The x-intercept is the point where a line crosses the x-axis. It is represented by the value of x when y is 0 in the equation of the line.

Front

What does a zero slope indicate?

Back

A zero slope indicates a horizontal line where the y-value remains constant as the x-value changes.