Exploring Linear Functions and Equations

This video tutorial covers linear functions, focusing on their unique characteristic of having a constant slope or rate of change. It explains the concept of slope, including positive and negative slopes, and how they relate to the increase or decrease of a function. The video also introduces two forms of linear equations: point-slope and slope-intercept forms, and demonstrates how to write equations using these forms. Several examples are provided to illustrate the concepts, including a final example of finding the equation of a line through two points.

What makes linear functions unique compared to other functions?

• Their multiple slopes

• Their variable rate of change

• Their constant rate of change

• Their ability to curve

In the first graph, what is the direction of the slope?

• Curved

• Downward

• Flat

• Upward

Which graph has a positive slope?

• Both the second and third graphs

• The first graph

• The third graph

• The second graph

What does the term 'rise over run' refer to?

• The horizontal change

• The vertical change

• The change in Y over the change in X

• The change in X over the change in Y

What symbol is often used to represent slope?

• M

• Y

• X

• B

What is the formula for point-slope form?

• y = mx + b

• y + y1 = m(x + x1)

• y - y1 = m(x - x1)

• y = mx - b

In slope-intercept form, what does 'B' represent?

• The slope

• The x-intercept

• The y-intercept

• The point

How do you write the equation of a line using function notation?

• f(x) = y + b

• y = f(x) + b

• f(x) = mx + b

• y = mx + b

What is the slope of the line in the first example?

• -2

• 4

• 1/2

• 3

What is the final equation of the line through the points (4, 2) and (1, -7)?

• y = 4x - 2

• y = 3x - 10

• y = 2x + 5

• y = -3x + 10