Comparing Linear Functions

Front

What is the slope of a linear function?

Back

The slope of a linear function is a measure of how steep the line is, representing the rate of change of the dependent variable (y) with respect to the independent variable (x). It is calculated as the change in y divided by the change in x.

Front

How do you identify the slope from the equation of a line in slope-intercept form (y = mx + b)?

Back

In the equation y = mx + b, 'm' represents the slope of the line.

Front

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

Back

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

Front

Given the equations y = 2x + 3 and y = 3x - 3, which has a higher slope?

Back

The equation y = 3x - 3 has a higher slope (3) compared to y = 2x + 3 (2).

Front

If a linear function has a negative slope, what does that indicate about the relationship between x and y?

Back

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

Front

What is the significance of the y-intercept in the equation y = 3x + 10?

Back

In this equation, the y-intercept is 10, which represents the monthly fee Rich pays before any visits to the gym.

Front

How can you determine which linear function has a higher y-intercept?

Back

Compare the constant term (b) in the slope-intercept form (y = mx + b); the function with the larger b value has a higher y-intercept.

Front

What does it mean if two linear functions have the same slope?

Back

If two linear functions have the same slope, they are parallel lines and will never intersect.

Front

In the context of weight loss, what does a steeper slope indicate?

Back

A steeper slope in a weight loss graph indicates a faster rate of weight loss.

Front

How do you find the total cost represented by a linear equation like y = 3x + 10?

Back

To find the total cost, substitute the number of visits (x) into the equation to calculate y.