# Slope and y intercept in real world examples

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Slope and y-intercept

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=2m= y2-y1 x2-x1

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

m= 14 7

9-(-5)/6-(-1) = 14/7 = 23

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.

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.69411363,d.cWc&psig=AFQjCNG7aTI3_c46Vjtpwqti1Q1nuwKY9w&ust=14034541298437145

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.69411363,d.cWc&psig=AFQjCNH-PbaE-PHj8KINJk8L7eNwAQ5uxQ&ust=14036391001565916

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.

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.69411363,d.cWc&psig=AFQjCNGe5v05S1tuuKciTJKkA8fWmp6PDQ&ust=14034546782349987

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.8

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 didnt 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-intercept2nd: 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 minutes4th: 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.

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.69411363,d.cWc&psig=AFQjCNEtADqtDT7vyOLKfYSVVLXyAS-gLQ&ust=14036384888830149