Understanding Slope and Intercept

The video tutorial explains how to determine the slope (m) and y-intercept (b) of a line from its graph. It demonstrates finding the y-intercept by identifying where the line crosses the y-axis and calculating the slope using vertical and horizontal changes between two points. An alternative method using a formula is also shown to verify the slope. Finally, the video illustrates how to write the equation of the line in slope-intercept form.

What are we asked to determine from the graph of the line?

• The slope and y-intercept of the line

• The length and width of the line

• The color and thickness of the line

• The area under the line

What is the y-intercept of the line given in the problem?

• (0, 5)

• (5, 0)

• (0, -5)

• (-5, 0)

How do we calculate the slope of a line using a graph?

• By adding the vertical and horizontal changes

• By multiplying the vertical change by the horizontal change

• By dividing the horizontal change by the vertical change

• By dividing the vertical change by the horizontal change

What is the vertical change between the points (0, -5) and (3, -1)?

• -4

• 4

• 3

• -3

What is the horizontal change between the points (0, -5) and (3, -1)?

• 3

• -3

• -4

• 4

What is the slope of the line calculated using the points (0, -5) and (3, -1)?

• 3/4

• -3/4

• 4/3

• -4/3

How can the slope be verified using the formula for change in y over change in x?

• By adding the y-coordinates and x-coordinates

• By subtracting the y-coordinates and dividing by the difference in x-coordinates

• By multiplying the y-coordinates and x-coordinates

• By dividing the x-coordinates by the y-coordinates

What is the result of the calculation: -1 minus -5?

• 6

• -6

• 4

• -4

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

• y = 3/4x + 5

• y = 3/4x - 5

• y = 4/3x - 5

• y = -4/3x + 5

Why is it more common to write 'minus 5' instead of 'plus negative 5' in the equation?

• It is mathematically incorrect to write 'plus negative 5'

• It simplifies the expression

• It is a rule in algebra

• It makes the equation longer