Understanding Slope from a Graph

The video tutorial explains how to estimate and interpret the slope of a line using a graph. It covers two methods: graphically determining the slope by calculating the vertical and horizontal changes between two points, and using the slope formula. The tutorial also interprets the slope in the context of a gas bill, explaining the rate of change in cost per therm of gas used. The video emphasizes understanding the slope's meaning by considering the changes in input and output values.

What is the primary purpose of finding the slope of a line on a graph?

• To identify the midpoint of the line

• To find the length of the line

• To determine the steepness of the line

• To calculate the area under the line

Which method can be used to find the slope of a line when given a graph?

• Using the midpoint formula

• Using the Pythagorean theorem

• Using the rise over run method

• Using the quadratic formula

If the vertical change is 55 and the horizontal change is 50, what is the slope of the line?

• 0.9

• 1.1

• 1.2

• 1.0

How can the slope 55/50 be simplified?

• 5/4

• 11/10

• 4/5

• 10/11

What is the formula used to verify the slope calculation?

• y2 - y1 / x2 - x1

• x2 - x1 / y2 - y1

• x1 + x2 / y1 + y2

• y1 + y2 / x1 + x2

What does the slope represent in the context of a gas bill and gas usage?

• The maximum gas bill

• The rate of change in cost per unit of gas used

• The total cost of gas

• The average gas usage

If the gas usage increases by 10 therms, how much does the gas bill increase according to the slope?

• 10 dollars

• 11 dollars

• 12 dollars

• 9 dollars

Which of the following is a correct interpretation of the slope 1.1 in the context of gas usage?

• 1.1 dollars per 10 therms

• 11 dollars per 100 therms

• 11 dollars per therm

• 1.1 dollars per therm

Why is it helpful to look at the denominator first when interpreting the slope?

• It measures the change in the output

• It measures the change in the input

• It provides the total change

• It simplifies the calculation

What does the numerator of the slope represent in the context of the gas bill?

• The change in gas usage

• The average gas usage

• The change in the gas bill

• The total gas bill