Rate of Change of Linear Function

What linear function is modeled by the data in the table?

• y = 3/8x - 1/8

• y = -1/8x + 1/2

• y = 3/8x

• none of the above

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

What is the slope of this linear relationship?

Answer explanation

The slope of a linear relationship is calculated as the change in y over the change in x. Here, the correct slope is m=-0.5, indicating a negative relationship where y decreases as x increases.

Tags

CCSS.8.EE.B.5

Find the slope:

Answer explanation

To find the slope, use the formula (change in y) / (change in x). The correct slope is \(\frac{4}{3}\), indicating a rise of 4 units for every run of 3 units, which matches the answer choice.

Tags

CCSS.8.EE.B.5

What is the slope formula?

• 
• 
• 
• 

Tags

CCSS.8.EE.B.5

Slope can be found by counting

______________.

• Rise over Run

• Run over Rise

Answer explanation

Slope is calculated as 'Rise over Run', which represents the vertical change (rise) divided by the horizontal change (run) between two points on a line. Therefore, the correct choice is 'Rise over Run'.

Tags

CCSS.8.EE.B.5

Answer explanation

To find the slope, use the formula \(\frac{y_2-y_1}{x_2-x_1}\). After substituting the values from the table, the calculation yields \(\frac{3}{1}\), which simplifies to 3. Thus, the correct answer is \(\frac{3}{1}\).

Tags

CCSS.8.EE.B.5

Find the rate of change.

• -2 minutes per gallon

• -20 minutes per gallon

• -2 gallons per minute

• -20 gallons per minute

Answer explanation

The rate of change is calculated as the change in gallons over the change in time. Here, it is -2 gallons per minute, indicating a decrease in gallons over time, making -2 gallons per minute the correct choice.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Use the graph to calculate the rate of change.

• 1

• -1

• 2

• -2

Answer explanation

The rate of change is calculated as the change in y divided by the change in x. From the graph, if y increases by 1 when x increases by 1, the rate of change is 1, making the correct answer 1.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Find the slope of the line.

• -2

• 2

• -1

• 1

Answer explanation

The slope of a line is calculated as the change in y over the change in x (rise/run). A slope of -1 indicates that for every unit increase in x, y decreases by 1. Thus, the correct answer is -1.

Tags

CCSS.8.EE.B.5

Find the slope of the line.

• Undefined

• 0

• 1

• -1

Answer explanation

The slope of a line is defined as the change in y over the change in x. A slope of 0 indicates a horizontal line, meaning there is no change in y as x changes. Therefore, the correct answer is 0.

Tags

CCSS.8.EE.B.5