Exploring Linear Functions and Slope

This video tutorial introduces linear functions and the concept of slope. It explains how linear functions can be represented graphically and describes the behavior of increasing, decreasing, and constant linear functions. The tutorial also covers the definition of slope as the ratio of change in output to change in input, and provides examples of calculating slope using two points on a graph.

What is the standard form of a linear function?

• f(x) = m/x + b

• f(x) = mx + b

• f(x) = mx^2 + b

• f(x) = ax^2 + bx + c

What does a positive slope indicate about a linear function?

• The function is decreasing.

• The function is constant.

• The function is increasing.

• The function is undefined.

What is the slope of a function that remains constant?

• Undefined

• Positive

• Zero

• Negative

How is slope calculated between two points?

• Sum of x coordinates over sum of y coordinates

• Change in y over change in x

• Change in x over change in y

• Sum of y coordinates over sum of x coordinates

What does an undefined slope indicate?

• The function is not linear.

• The function is constant.

• The function is decreasing.

• The function is increasing.

If a line goes downhill from left to right, what is the slope?

• Negative

• Positive

• Undefined

• Zero

What does the slope of -2/3 indicate about a line's direction?

• Vertical line

• Horizontal line

• Downhill from left to right

• Uphill from left to right

What slope value indicates a horizontal line?

• Zero

• Negative

• Positive

• Undefined

In the slope formula, what does Δy/Δx represent?

• Sum of x coordinates over sum of y coordinates

• Sum of y coordinates over sum of x coordinates

• Change in y over change in x

• Change in x over change in y

What does a slope of 3/7 tell us about the function's behavior?

• It increases slowly.

• It decreases rapidly.

• It remains constant.

• It is not linear.