Slope of Proportional Graphs & Tables

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in the vertical direction (rise) divided by the change in the horizontal direction (run).

Front

What does the point (0,0) represent in a proportional graph?

Back

The point (0,0) represents the origin, indicating that no quantity of the dependent variable is produced when there is no quantity of the independent variable.

Front

If a graph shows a slope of 2, what does this mean in a real-world context?

Back

A slope of 2 means that for every 1 unit increase in the independent variable, the dependent variable increases by 2 units.

Front

What is a unit rate?

Back

A unit rate is a comparison of two different quantities when they are combined together, expressed as a quantity per 1 unit of another quantity.

Front

How do you calculate the slope from a table of values?

Back

To calculate the slope from a table, take two points (x1, y1) and (x2, y2) and use the formula: slope = (y2 - y1) / (x2 - x1).

Front

What does a slope of 0 indicate about a graph?

Back

A slope of 0 indicates a horizontal line, meaning there is no change in the dependent variable as the independent variable changes.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as the independent variable increases, the dependent variable decreases.

Front

In the context of saving money, what does a higher slope represent?

Back

A higher slope represents a greater amount of money saved per unit of time.

Front

What is the significance of the y-intercept in a proportional graph?

Back

The y-intercept indicates the value of the dependent variable when the independent variable is zero.

Front

How can you determine who saves more money from a graph?

Back

You can determine who saves more money by comparing the slopes of their respective lines; the steeper line indicates more savings per time unit.