Slope Applications

Front

What is the slope in a linear relationship?

Back

The slope represents the rate of change between two variables, indicating how much one variable changes for a unit change in another variable.

Front

How do you calculate the slope from two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate about a graph?

Back

A positive slope indicates that as one variable increases, the other variable also increases.

Front

What does a negative slope indicate about a graph?

Back

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

Front

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

Back

The y-intercept is the value of y when x is 0, representing the starting point of the relationship.

Front

If a taxi charges $0.30 per mile, what is the slope of the cost vs. miles graph?

Back

The slope is $0.30 per mile.

Front

If a candle decreases in height by 1/10 of an inch every minute, what is the slope of the height vs. time graph?

Back

The slope is -1/10 inches per minute.

Front

What does it mean if the slope of a graph is zero?

Back

A slope of zero indicates that there is no change in the dependent variable as the independent variable changes; the graph is a horizontal line.

Front

How can you interpret the slope in a real-world context?

Back

The slope can be interpreted as the rate of change, such as speed, cost per unit, or growth rate.

Front

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

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.