Understanding Proportional Relationships and Rates

Front

What is a proportional relationship?

Back

A proportional relationship is a relationship between two quantities where the ratio of one quantity to the other quantity is constant.

Front

Define the constant of proportionality (k).

Back

The constant of proportionality (k) is the constant value that relates two proportional quantities, expressed as k = y/x.

Front

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

Back

The slope (m) of a line through two points (x1, y1) and (x2, y2) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x, indicating how steep the line is.

Front

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

Back

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

Front

How can you determine if a deal is better based on unit price?

Back

To determine if a deal is better, calculate the unit price by dividing the total cost by the total weight or quantity. The lower the unit price, the better the deal.

Front

What is the relationship between slope and rate of change?

Back

The slope of a line is a measure of the rate of change between two variables; a steeper slope indicates a greater rate of change.

Front

What does a slope of 0 indicate about a line?

Back

A slope of 0 indicates that the line is horizontal, meaning there is no change in y as x changes.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as one variable increases, the other variable decreases, showing an inverse relationship.

Front

How do you interpret 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.