Interpreting Slope - Wangen

Front

What is the definition of slope in a linear function?

Back

The slope of a linear function is a measure of the steepness or incline of the line, represented as the ratio of the change in the y-coordinate to the change in the x-coordinate (rise over run).

Front

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

Back

The slope (m) is calculated using the formula: m = \frac{y2 - y1}{x2 - x1}.

Front

What does a positive slope indicate about a linear function?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, showing a direct relationship.

Front

What does a negative slope indicate about a linear function?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, showing an inverse relationship.

Front

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

Back

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

Front

What does the y-intercept represent in a linear function?

Back

The y-intercept represents the value of y when x is 0, indicating where the line crosses the y-axis.

Front

In the context of a real-world scenario, what does the slope represent?

Back

In real-world scenarios, the slope often represents a rate of change, such as speed, cost per item, or growth rate.

Front

If a car salesman earns a commission of $425 per car sold, what is the slope of his earnings function?

Back

The slope of his earnings function is $425/car, representing the commission earned per car sold.

Front

If the cost of renting a car increases by $12 per hour, what does this indicate about the slope?

Back

This indicates that the slope is $12/hour, representing the increase in cost for each additional hour rented.

Front

What does a slope of $0.25 per paper delivered mean for a paperboy's earnings?

Back

It means the paperboy earns $0.25 for each paper he delivers.