Unit 10: Linear Relationships Study Guide

Front

What does it mean for a relationship to be proportional?

Back

A proportional relationship is one in which two quantities maintain a constant ratio, meaning that as one quantity increases or decreases, the other does so in a consistent manner.

Front

What is the definition of slope in a linear relationship?

Back

The slope (m) of a linear relationship represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It is calculated as the rise over run between two points on the line.

Front

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

Back

The y-intercept (b) is the value of y when x is 0. It represents the point where the line crosses the y-axis.

Front

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

Back

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

Front

How can you determine if a graph represents a proportional relationship?

Back

A graph represents a proportional relationship if it is a straight line that passes through the origin (0,0).

Front

What is the formula to calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The formula to calculate the slope (m) is m = (y2 - y1) / (x2 - x1).

Front

What does it mean if a relationship is 'not proportional'?

Back

A relationship is 'not proportional' if the ratio between the two quantities is not constant, meaning that the graph does not pass through the origin or is not a straight line.

Front

What is the significance of the slope in real-world applications?

Back

The slope can represent various real-world rates, such as speed (distance over time) or cost per item, indicating how one quantity changes in relation to another.

Front

How do you find the equation of a line given two points?

Back

To find the equation of a line given two points, first calculate the slope using the slope formula, then use one of the points to solve for the y-intercept, and finally write the equation in slope-intercept form.

Front

What is the relationship between the slope and the steepness of a line?

Back

The slope indicates the steepness of a line; a larger absolute value of the slope means a steeper line, while a slope of zero indicates a horizontal line.