Understanding Linear Functions

The video tutorial explains how to determine the slope, vertical intercept, and equation of a linear function from its graph. It begins by identifying two points on the graph to calculate the slope using the change in y over the change in x. The tutorial then verifies the slope using alternative points. It identifies the vertical intercept and uses this information to write the equation of the line in slope-intercept form, y = mx + b.

What are the three main tasks we need to accomplish with the given linear function graph?

• Find the slope, midpoint, and equation

• Find the slope, vertical intercept, and equation

• Find the slope, horizontal intercept, and equation

• Find the slope, axis of symmetry, and equation

Which two points are used to initially calculate the slope of the line?

• (0, 4000) and (200, 0)

• (0, 0) and (200, 4000)

• (100, 2000) and (80, 2400)

• (0, 200) and (4000, 0)

What is the calculated slope using the points (0, 4000) and (200, 0)?

• 10

• 20

• -20

• -10

Which two points are used to verify the slope calculation?

• (0, 200) and (4000, 0)

• (0, 0) and (200, 4000)

• (100, 2000) and (80, 2400)

• (0, 4000) and (200, 0)

What is the slope calculated using the points (80, 2400) and (100, 2000)?

• -20

• -10

• 10

• 20

Where does the line intersect the vertical axis?

• (4000, 0)

• (200, 0)

• (0, 4000)

• (0, 0)

What is the value of the vertical intercept?

• 200

• 4000

• 0

• -20

What is the slope-intercept form of the equation for the line?

• y = 20x - 4000

• y = -20x - 4000

• y = 20x + 4000

• y = -20x + 4000

What does the 'b' in the slope-intercept form y = mx + b represent?

• The horizontal intercept

• The midpoint of the line

• The vertical intercept

• The slope of the line

If the slope of a line is -20, what does this indicate about the line's direction?

• The line slopes upward

• The line is vertical

• The line slopes downward

• The line is horizontal