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 is constant.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the y-coordinate with respect to the x-coordinate.

Front

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

Back

The formula is (y2 - y1) / (x2 - x1).

Front

What is an undefined slope?

Back

An undefined slope occurs when a line is vertical, meaning it goes straight up and down.

Front

What is a constant rate of change?

Back

A constant rate of change means that for every unit increase in one quantity, there is a consistent increase in another quantity.

Front

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

Back

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

Front

What does it mean if a relationship is not proportional?

Back

If a relationship is not proportional, the ratio between the two quantities is not constant.

Front

Find the slope of the line that passes through the points (1, 2) and (3, 6).

Back

The slope is 2.

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

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

Back

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