Linear Relationships Study Guide

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 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 the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Front

How do you calculate 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 a line?

Back

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

Front

What does it mean if a line has an undefined slope?

Back

A line has an undefined slope if it is vertical, meaning it goes straight up and down. This occurs when the x-coordinates of two points on the line are the same.

Front

What is the difference between positive and negative slope?

Back

A positive slope means that as x increases, y also increases, resulting in an upward slant. A negative slope means that as x increases, y decreases, resulting in a downward slant.

Front

If two lines have the same slope, what can be said about their relationship?

Back

If two lines have the same slope, they are parallel and will never intersect.

Front

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

Back

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

Front

How can you determine if two triangles lie on the same line?

Back

Two triangles can lie on the same line if they have the same slope. If their slopes are different, they cannot lie on the same line.

Front

What is a horizontal line's slope?

Back

A horizontal line has a slope of 0, meaning there is no change in y as x changes.