Slippery SlopesA lesson on interpreting slope and y-intercept

in real world examples

Standard:MAFS.912.S-ID.3.7:

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

Problem of the Day:

Solve for the slope between (-1,-5) and (6,9).

m=2

m= y2-y1 x2-x1

m= 9-(-1) 6-(-1)

m= 14 7

VocabularySlope intercept form- y=mx+b, where m is slope and b is the y-intercept

Slope- Change in y over change in x (rate of change)

Y-intercept- the value of y when x is zero

Example of Slope in a Real World Scenario

m= Change in height Change in time

The graph to the right shows the growth of a tree at a constant rate, over a period of four years. Interpret the slope of the line.

Example of Slope in a Real World Scenario

m= change in distance change in time

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Example of Y-Intercept in a Real World Scenario.

For example: The y-intercept in this graph is 1080, meaning it is the amount the person owes before he/she began making payments. (zero payments have been made, $1080 owed)

The graph then shows that over the next 24 months this debt will be paid off.

Example of Y-Intercept in a Real World Scenario

You have 300 items of clothing and decide to start donating to Goodwill. Your y-intercept is the amount of clothing you have before you start donating to Goodwill every month.

Solving a Real World ExampleA student is eating an ice

cream cone at the park that is 12.7cm tall. It is extremely hot outside and the ice cream starts to melt at a constant rate of 2cm/minute. If the student didn’t eat any of the ice cream and it started to melt, how much would be left after 3 minutes?

1st: Identify the slope and y-intercept

2nd: Plug into slope intercept formY=-2x+12.7 (slope is

negative because it is decreasing in size)

3rd: Plug in 3 for x since we want to know how tall it will be after 3 minutes

4th: Solvey=-2(3)+12.7y=-6+12.7y=6.7

Understand that after 3 minutes of melting the ice cream cone will now measure 6.7cm.