Understanding Linear Functions and Slope

This video tutorial introduces linear functions and the concept of slope. It defines linear functions as those that can be represented by a straight line on a coordinate plane and explains the behavior of these functions as increasing, decreasing, or constant. The tutorial also covers the concept of slope, describing it as the ratio of the change in output to the change in input, and provides examples of how to calculate slope using two points on a line.

What is the general form of a linear function?

• f(x) = ax + b^2

• f(x) = a/x + b

• f(x) = mx + b

• f(x) = ax^2 + bx + c

How is an increasing linear function graphically represented?

• A line going downhill from left to right

• A horizontal line

• A vertical line

• A line going uphill from left to right

What does a constant linear function look like on a graph?

• A vertical line

• A line going uphill

• A horizontal line

• A line going downhill

What is the slope of a line that is horizontal?

• Negative

• Positive

• Undefined

• Zero

How is the slope of a line defined?

• The product of the changes in x and y

• The sum of the changes in x and y

• The ratio of the change in output to the change in input

• The ratio of the change in x to the change in y

If a line has a negative slope, what does it indicate?

• The line is vertical

• The line is decreasing

• The line is increasing

• The line is horizontal

What is the slope of a vertical line?

• Positive

• Negative

• Zero

• Undefined

In the example with points (-2, 3) and (4, -1), what is the simplified slope?

• 2/3

• 3/2

• -2/3

• -3/2

For a line passing through points (3, 2) and (-1, 2), what is the slope?

• Negative

• Zero

• Undefined

• Positive

What happens to the slope when the change in input is zero?

• The slope is positive

• The slope is negative

• The slope is zero

• The slope is undefined