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 a linear equation of 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 the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is and the direction it goes (upward or downward).

Front

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What does an undefined slope indicate?

Back

An undefined slope indicates a vertical line, where the change in x is zero, meaning the line does not have a defined slope.

Front

What does a positive slope indicate about a linear relationship?

Back

A positive slope indicates that as the independent variable (x) increases, the dependent variable (y) also increases.

Front

What does a negative slope indicate about a linear relationship?

Back

A negative slope indicates that as the independent variable (x) increases, the dependent variable (y) decreases.

Front

What is the y-intercept in a linear equation?

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 equation of a line is y = 3x + 2, what is the slope?

Back

The slope of the line is 3.

Front

If a line has a slope of 0, what does that mean?

Back

A slope of 0 means the line is horizontal, indicating that there is no change in the dependent variable (y) as the independent variable (x) changes.

Front

What is the formula for finding the y-value given an x-value in a linear equation?

Back

To find the y-value, substitute the x-value into the linear equation y = mx + b.