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**A lesson on interpreting slope and y-intercept in real world examples**

Slippery Slopes A lesson on interpreting slope and y-intercept in real world examples

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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.

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**Problem of the Day: m=2 Solve for the slope between (-1,-5) and (6,9).**

m= y2-y1 x2-x1 m= 9-(-1) 6-(-1) m= 14 7 9-(-5)/6-(-1) = 14/7 = 2 m=2

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Vocabulary Slope 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

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**Example of Slope in a Real World Scenario**

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. This image was found at: https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=QKIyhPMIyNtI9M&tbnid=NDEOL0eiQyQ_mM:&ved=0CAQQjB0&url=http%3A%2F%2Fen.wikipedia.org%2Fwiki%2FMisleading_graph&ei=TbGlU-jyFY3jsATZy4LgDw&bvm=bv ,d.cWc&psig=AFQjCNG7aTI3_c46Vjtpwqti1Q1nuwKY9w&ust= m= Change in height Change in time

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**Example of Slope in a Real World Scenario**

m= change in distance change in time The image was found at: https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=Fuh88Lnfqe57KM&tbnid=QsX4GcQ8OeRGBM:&ved=0CAQQjB0&url=http%3A%2F%2Fen.wikiversity.org%2Fwiki%2FMotion_-_Kinematics&ei=xIOoU5j1AYSdyASc1IK4Aw&bvm=bv ,d.cWc&psig=AFQjCNH-PbaE-PHj8KINJk8L7eNwAQ5uxQ&ust=

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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) This image was found at: https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=X6xsXeHwGLrLuM&tbnid=J-zd-Jb38yyezM:&ved=0CAQQjB0&url=http%3A%2F%2Fwww.montereyinstitute.org%2Fcourses%2FDevelopmentalMath%2FCOURSE_TEXT2_RESOURCE%2FU13_L1_T2_text_final.html&ei=Z7OlU9b-DqqqsQTiqYHgBg&bvm=bv ,d.cWc&psig=AFQjCNGe5v05S1tuuKciTJKkA8fWmp6PDQ&ust= The graph then shows that over the next 24 months this debt will be paid off.

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**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. Graph was created using Geogebra.

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**Solving a Real World Example**

A 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 form Y=-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: Solve y=-2(3)+12.7 y= y=6.7 The image was found at: https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=_kteaVXedFWAqM&tbnid=FdgMX9o2die0lM:&ved=0CAQQjB0&url=http%3A%2F%2Fwww.bentnorthrop.org%2F%3Fattachment_id%3D1120&ei=iYGoU4qBMs_MsQTZ-oLoDg&bvm=bv ,d.cWc&psig=AFQjCNEtADqtDT7vyOLKfYSVVLXyAS-gLQ&ust= Understand that after 3 minutes of melting the ice cream cone will now measure 6.7cm.

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**Leaky Lines Project Items you should have: 400ml of water**

500ml+ graduated cylinder Empty water bottle Stopwatch This image was found at: https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=jfWfZe1AG2_lvM&tbnid=ILFl8EqkpQCr5M:&ved=0CAQQjB0&url=http%3A%2F%2Fwww.physicslessons.com%2Fmicrolabsa.htm&ei=k0SoU_PqHczgsAT9s4CgBw&bvm=bv ,d.cWc&psig=AFQjCNG8a7WA_3JqUSqypdwX1_P7g48qrA&ust=

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**Leaky Lines Project Get into groups of two Measure 400ml into bottle**

One person will hold the water bottle and be in charge of the stopwatch Measure 400ml into bottle Turn water bottle over and start timer Every 10 seconds record how much water has accumulated in the cylinder Image was found at: https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=dTkT0-dNr8UvYM&tbnid=WxmkuPjN-JP-_M:&ved=0CAQQjB0&url=http%3A%2F%2Flivinginkaohsiung.blogspot.com%2F2013%2F01%2Fwindow-farming-wicking-method.html&ei=_EWoU_OsBbOhsAS3xoGwDQ&bvm=bv ,d.cWc&psig=AFQjCNGTfJ9-yxuH_or6DVjUb5cCDiKsMQ&ust=

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Leaky Lines Project Create a graph based on the data gathered graphing the time intervals on the x-axis and the amount of milliliters on the y-axis. Solve for the rate of change between two coordinates. Write the equation of the line. Discussion: Is the slope positive or negative? What is the y-intercept?

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Independent Practice Had we been measuring the rate at which the water left the bottle, would the slope have been positive or negative? What would the y-intercept have been? Write an equation expressing this linear relationship using m for slope. This image was found at: https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&docid=gkYaj0LWF3LMbM&tbnid=FIwFDeo4wmI42M:&ved=0CAQQjB0&url=http%3A%2F%2Fwww.shelovesmath.com%2Falgebra%2Fbeginning-algebra%2Fcoordinate-system-and-graphing-lines%2F&ei=8sWoU_aJJsa_sQSa7YKgAg&bvm=bv ,d.cWc&psig=AFQjCNHncecUwN6XNN0-9b6ZNLIHm4bpWA&ust=

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Review for Quiz Your family is taking a trip to Disney and is driving at a constant rate. After one hour, you have traveled 60 miles, and after 2 hours you have traveled 120 miles. How fast is the car going? You are selling candy bars for a fundraiser. You have raised $50 so far and sell each candy bar for 75 cents. How much money will you have made after selling 30 candy bars? Answer Key: (1,60) and (2,120). Solve for rate of change. m= /2-1. m=60. The rate of change is 60, therefore the car is traveling at 60mph. The equation representing this word problem is y=.75x+50. Plug in 30 for x to solve for y, the total amount of money raised. y=.75(30)+50. y=72.50

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**Review for Quiz Continued**

The graph shows the amount of money you have at the beginning of the month. a. How much money did you begin with? b. How much money do you earn each week? c. How much money will you have after 3 weeks? You begin with $5. This can be found by looking at the y-intercept, when x is 0 y is 5. By looking at the graph you can calculate the slope between two coordinates. The line rises up 3 and runs over 1, therefore m=3. The equation of the line represented in this graph is y=3x+5. In order to find out how much money you will have after three weeks, plug in a 3 for x and solve for y, the total amount of money. Y=3(3)+5, y=14. You will have $14 in 3 weeks.

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