Interpret the meaning of Slope from a Graph

Front

What does the slope of a graph represent in a real-world context?

Back

The slope represents the rate of change between two variables, indicating how one variable changes in relation to another.

Front

Define slope in mathematical terms.

Back

Slope is defined as the ratio of the change in the y-coordinate to the change in the x-coordinate (rise/run).

Front

What is the formula to calculate the slope of a line?

Back

Slope (m) = (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are two points on the line.

Front

If a graph shows a constant slope, what does that indicate about the relationship between the variables?

Back

A constant slope indicates a linear relationship between the variables, meaning they change at a consistent rate.

Front

In the context of a moving truck rental, what does a slope of $0.50 per mile mean?

Back

It means that for every mile driven, the cost increases by $0.50.

Front

What does a steeper slope indicate compared to a less steep slope?

Back

A steeper slope indicates a greater rate of change between the two variables.

Front

How can you interpret a negative slope on a graph?

Back

A negative slope indicates that as one variable increases, the other variable decreases.

Front

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

Back

The y-intercept represents the value of y when x is zero, indicating the starting point of the relationship.

Front

If a graph shows that $500 is earned for every 8 hours worked, what is the slope?

Back

The slope is $500/8 hours = $62.50 per hour.

Front

What does the slope of a graph representing distance vs. gasoline used indicate?

Back

The slope indicates the fuel efficiency of the vehicle, measured in distance per gallon.