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, typically described by the equation 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 or incline of the line, calculated as the change in y (rise) divided by the change in x (run). It is often represented by the letter m.

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 does a zero slope indicate?

Back

A zero slope indicates that the line is horizontal, meaning there is no change in y as x changes; the y-value remains constant.

Front

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

Back

The y-intercept can be found by setting x to 0 in the linear equation y = mx + b, resulting in the value of b.

Front

What is the formula to calculate the slope between two points?

Back

The formula to calculate the slope (m) between two points (x1, y1) and (x2, y2) is m = (y2 - y1) / (x2 - x1).

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is 0.

Front

What is the difference between a positive slope and a negative slope?

Back

A positive slope rises from left to right, while a negative slope falls from left to right.

Front

What does it mean if a line is vertical?

Back

A vertical line has an undefined slope and indicates that the x-value is constant while the y-value can change.