Rate of Change

Rate of Change

I can find the rate of change in tables, graphs, and equations

Let's Review What We Learned

• ​The table below shows a linear relationship between the time that has passed since the candle was lit and the height of a candle.  What is the rate of change of the height of the candle with respect to time?

• ​height of the candle is the y-value

• ​time is the x-value

• ​Pick 2 points

• ​Find the Change in y

• ​Find the Change in x

• ​Divide the two values to find the rate of change (slope of the line).

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The table below shows a linear relationship between x and y.  What is the rate of change of y with respect to x? 

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 The graph below shows the relationship between hours worked and tips earned for a carhop at Sonic.  What is the ROC?

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The graph shows the relationship between hours spent gaming in a week and class average.

What is the rate of change?

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The table below shows a linear relationship between x and y.  What is the rate of change of y with respect to x?

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The table below shows a linear relationship between the average height of a diving platform and the amount of time, in seconds, it takes for the diver to break the surface of the water.  What is the rate of change of the average time in seconds with respect to the height of the diving platform?

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Rate of Change from Equations

Multiple Choice

What is step 1 when we are changing from standard form to slope-intercept form?

• Move the x-term

• Divide 

• Move the y-term

• Multiply

Multiple Choice

When converting the equation

2x + 4y = 8

into slope-intercept form, the first step to solve for y would be to ____________.

• subtract 2x from each side

• subtract 4y from each side

• add 2x to each side

• add 4y to each side

Multiple Choice

After subtracting 2x from each side, the resulting equation is shown below:

2x + 4y = 8

4y = -2x + 8

The final step to solve for y would be to ____________.

• divide each term by 4

• divide each term by -4

• add 4 to each side

• subtract 4 from each side

Multiple Choice

Solve for y:

5x + y = -10

• y = 5x + 10
• y = -5x - 10

Multiple Choice

What is the slope for this function?

3x + y = 12

• m = -3

• m = 1

• m = 12

• m = 3

Multiple Choice

What is the slope for this f

x + y = 4

• m = 1

• m = -1

• m = 4

• m = -4

Multiple Choice

• y=-3x+1

• y=3x+1

• y=1/3x+1

• y=-1/3x-1

Multiple Choice

• y=-4x-12

• y=4x+12

• y=-4x+12

• y=-4x+3