Understanding Slope from a Graph

The video tutorial explains the concept of slope in a graph, detailing how it represents the rate of change between the output and input variables. It covers the direction of slope, indicating whether it is positive or negative, and provides formulas for calculating slope. The tutorial demonstrates how to find the slope using a graph by selecting two points and calculating the vertical and horizontal changes. It also shows how to use the slope formula to achieve the same result, emphasizing the graphical interpretation of slope as a consistent pattern of movement along the line.

What does the slope of a line represent in a graph?

• The rate of change of the output variable with respect to the input variable

• The total length of the line

• The color of the line

• The width of the line

If a line is slanted downhill from left to right, what can be said about its slope?

• The slope is zero

• The slope is positive

• The slope is negative

• The slope is undefined

Which formula is used to express the slope of a line?

• Slope = y divided by x

• Slope = x divided by y

• Slope = change in x divided by change in y

• Slope = change in y divided by change in x

What is one method to find the slope of a line from its graph?

• Measure the length of the line

• Select two points and calculate the vertical and horizontal changes

• Count the number of grid squares the line crosses

• Estimate the slope by eye

When using the slope formula, what does the difference in y-coordinates represent?

• The change in input

• The midpoint of the line

• The change in output

• The total distance

In the example, what is the vertical change between the two points?

• -6 units

• 6 units

• -40 units

• 40 units

How is the slope simplified in the example calculation?

• By multiplying the numerator and denominator by 2

• By subtracting 2 from both the numerator and denominator

• By dividing the numerator and denominator by 2

• By adding 2 to both the numerator and denominator

What does the slope of -20/3 indicate about the line's behavior?

• The line is horizontal

• The output increases by 20 for every increase of 3 in the input

• The line is vertical

• The output decreases by 20 for every increase of 3 in the input

How can you verify the slope using the slope formula?

• By checking if the line is straight

• By comparing the calculated slope with the graphical movement between points

• By measuring the angle of the line

• By counting the number of points on the line

What does moving down 20 units and right 3 units on the graph indicate?

• Finding a new point on the line

• Increasing the length of the line

• Changing the slope of the line

• Decreasing the width of the line