Finding a linear function
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Transcript of Finding a linear function
![Page 1: Finding a linear function](https://reader033.fdocuments.in/reader033/viewer/2022060202/559d06291a28ab5d698b47ad/html5/thumbnails/1.jpg)
Finding the formula of a linear function
f(x ) = mx + b
![Page 2: Finding a linear function](https://reader033.fdocuments.in/reader033/viewer/2022060202/559d06291a28ab5d698b47ad/html5/thumbnails/2.jpg)
f(x) = mx + b
• In August, you used 5 therms of natural gas, and your gas bill was $13.25. In January, you used 38 therms of natural gas and your gas bill was $54.50.
![Page 3: Finding a linear function](https://reader033.fdocuments.in/reader033/viewer/2022060202/559d06291a28ab5d698b47ad/html5/thumbnails/3.jpg)
f(x) = mx + b
• In August, you used 5 therms of natural gas, and your gas bill was $13.25. In January, you used 38 therms of natural gas and your gas bill was $54.50.
• Find the equation of the linear function G(t) that determines your monthly gas bill G based on the number of therms of gas t.
![Page 4: Finding a linear function](https://reader033.fdocuments.in/reader033/viewer/2022060202/559d06291a28ab5d698b47ad/html5/thumbnails/4.jpg)
G(t) = mt + b
• In August, you used 5 therms of natural gas, and your gas bill was $13.25. In January, you used 38 therms of natural gas and your gas bill was $54.50.
• Find the equation of the linear function G(t) that determines your monthly gas bill G based on the number of therms of gas t.
![Page 5: Finding a linear function](https://reader033.fdocuments.in/reader033/viewer/2022060202/559d06291a28ab5d698b47ad/html5/thumbnails/5.jpg)
G(t) = mt + b
• In August, you used 5 therms of natural gas, and your gas bill was $13.25. In January, you used 38 therms of natural gas and your gas bill was $54.50.
• Find the equation of the linear function G(t) that determines your monthly gas bill G based on the number of therms of gas t.
• This means that we have to find a slope and a y-intercept
![Page 6: Finding a linear function](https://reader033.fdocuments.in/reader033/viewer/2022060202/559d06291a28ab5d698b47ad/html5/thumbnails/6.jpg)
G(t) = mt + b
• August: 5 therms; $13.25• January,: 38 therms; $54.50
![Page 7: Finding a linear function](https://reader033.fdocuments.in/reader033/viewer/2022060202/559d06291a28ab5d698b47ad/html5/thumbnails/7.jpg)
G(t) = mt + b
• August: 5 therms; $13.25• January,: 38 therms; $54.50
• To find the slope, it might be helpful to draw a graph:
![Page 8: Finding a linear function](https://reader033.fdocuments.in/reader033/viewer/2022060202/559d06291a28ab5d698b47ad/html5/thumbnails/8.jpg)
G(t) = mt + b
• August: 5 therms; $13.25• January,: 38 therms; $54.50
• To find the slope, it might be helpful to draw a graph:
![Page 9: Finding a linear function](https://reader033.fdocuments.in/reader033/viewer/2022060202/559d06291a28ab5d698b47ad/html5/thumbnails/9.jpg)
G(t) = mt + b
• August: 5 therms; $13.25• January,: 38 therms; $54.50
• To find the slope, it might be helpful to draw a graph:
therms
charge
![Page 10: Finding a linear function](https://reader033.fdocuments.in/reader033/viewer/2022060202/559d06291a28ab5d698b47ad/html5/thumbnails/10.jpg)
G(t) = mt + b
• August: 5 therms; $13.25• January,: 38 therms; $54.50
• To find the slope, it might be helpful to draw a graph:
therms
charge
5
13.25
![Page 11: Finding a linear function](https://reader033.fdocuments.in/reader033/viewer/2022060202/559d06291a28ab5d698b47ad/html5/thumbnails/11.jpg)
G(t) = mt + b
• August: 5 therms; $13.25• January,: 38 therms; $54.50
• To find the slope, it might be helpful to draw a graph:
therms
charge
5
13.25
38
54.50
![Page 12: Finding a linear function](https://reader033.fdocuments.in/reader033/viewer/2022060202/559d06291a28ab5d698b47ad/html5/thumbnails/12.jpg)
f(x) = mx + b
• August: 5 therms; $13.25• January,: 38 therms; $54.50
• To find the slope, we need a rise
therms
charge
5
13.25
38
54.50
![Page 13: Finding a linear function](https://reader033.fdocuments.in/reader033/viewer/2022060202/559d06291a28ab5d698b47ad/html5/thumbnails/13.jpg)
f(x) = mx + b
• August: 5 therms; $13.25• January,: 38 therms; $54.50
• To find the slope, we need a rise
therms
charge
5
13.25
38
54.50
![Page 14: Finding a linear function](https://reader033.fdocuments.in/reader033/viewer/2022060202/559d06291a28ab5d698b47ad/html5/thumbnails/14.jpg)
f(x) = mx + b
• August: 5 therms; $13.25• January,: 38 therms; $54.50
• To find the slope, we need a rise
therms
charge
5
13.25
38
54.50
41.25
![Page 15: Finding a linear function](https://reader033.fdocuments.in/reader033/viewer/2022060202/559d06291a28ab5d698b47ad/html5/thumbnails/15.jpg)
G(t) = mt + b
• August: 5 therms; $13.25• January,: 38 therms; $54.50
• To find the slope, we need a rise and a run
therms
charge
5
13.25
38
54.50
41.25
![Page 16: Finding a linear function](https://reader033.fdocuments.in/reader033/viewer/2022060202/559d06291a28ab5d698b47ad/html5/thumbnails/16.jpg)
G(t) = mt + b
• August: 5 therms; $13.25• January,: 38 therms; $54.50
• To find the slope, we need a rise and a run
therms
charge
5
13.25
38
54.50
41.25
![Page 17: Finding a linear function](https://reader033.fdocuments.in/reader033/viewer/2022060202/559d06291a28ab5d698b47ad/html5/thumbnails/17.jpg)
G(t) = mt + b
• August: 5 therms; $13.25• January,: 38 therms; $54.50
• To find the slope, we need a rise and a run
therms
charge
5
13.25
38
54.50
41.2533
![Page 18: Finding a linear function](https://reader033.fdocuments.in/reader033/viewer/2022060202/559d06291a28ab5d698b47ad/html5/thumbnails/18.jpg)
G(t) = mt + b
• August: 5 therms; $13.25• January,: 38 therms; $54.50
• The slope is
therms
charge
5
13.25
38
54.50
41.2533
![Page 19: Finding a linear function](https://reader033.fdocuments.in/reader033/viewer/2022060202/559d06291a28ab5d698b47ad/html5/thumbnails/19.jpg)
G(t) = mt + b
• August: 5 therms; $13.25• January,: 38 therms; $54.50
• The slope is which is
therms
charge
5
13.25
38
54.50
41.2533
![Page 20: Finding a linear function](https://reader033.fdocuments.in/reader033/viewer/2022060202/559d06291a28ab5d698b47ad/html5/thumbnails/20.jpg)
G(t) = mt + b
• August: 5 therms; $13.25• January,: 38 therms; $54.50
• The slope is which is = 1.25
therms
charge
5
13.25
38
54.50
41.2533
![Page 21: Finding a linear function](https://reader033.fdocuments.in/reader033/viewer/2022060202/559d06291a28ab5d698b47ad/html5/thumbnails/21.jpg)
G(t) = 1.25t + b
• August: 5 therms; $13.25• January,: 38 therms; $54.50
• We found the slope
![Page 22: Finding a linear function](https://reader033.fdocuments.in/reader033/viewer/2022060202/559d06291a28ab5d698b47ad/html5/thumbnails/22.jpg)
G(t) = 1.25t + b
• August: 5 therms; $13.25• January,: 38 therms; $54.50
• We found the slope, now we need to find the y-intercept
![Page 23: Finding a linear function](https://reader033.fdocuments.in/reader033/viewer/2022060202/559d06291a28ab5d698b47ad/html5/thumbnails/23.jpg)
G(t) = 1.25t + b
• August: 5 therms; $13.25• January,: 38 therms; $54.50
• One way to find the y-intercept is to pick one of the two months
![Page 24: Finding a linear function](https://reader033.fdocuments.in/reader033/viewer/2022060202/559d06291a28ab5d698b47ad/html5/thumbnails/24.jpg)
G(t) = 1.25t + b
• August: 5 therms; $13.25• January,: 38 therms; $54.50
• One way to find the y-intercept is to pick one of the two months (let’s say August)
![Page 25: Finding a linear function](https://reader033.fdocuments.in/reader033/viewer/2022060202/559d06291a28ab5d698b47ad/html5/thumbnails/25.jpg)
G(t) = 1.25t + b
• August: 5 therms; $13.25• January,: 38 therms; $54.50
• One way to find the y-intercept is to pick one of the two months (let’s say August) and plug in the number of therms and the charge.
![Page 26: Finding a linear function](https://reader033.fdocuments.in/reader033/viewer/2022060202/559d06291a28ab5d698b47ad/html5/thumbnails/26.jpg)
G(t) = 1.25t + b
• August: 5 therms; $13.25• January,: 38 therms; $54.50
• One way to find the y-intercept is to pick one of the two months (let’s say August) and plug in the number of therms and the charge.
![Page 27: Finding a linear function](https://reader033.fdocuments.in/reader033/viewer/2022060202/559d06291a28ab5d698b47ad/html5/thumbnails/27.jpg)
G(t) = 1.25t + b
• August: 5 therms; $13.25• January,: 38 therms; $54.50
• One way to find the y-intercept is to pick one of the two months (let’s say August) and plug in the number of therms and the charge.
![Page 28: Finding a linear function](https://reader033.fdocuments.in/reader033/viewer/2022060202/559d06291a28ab5d698b47ad/html5/thumbnails/28.jpg)
G(t) = 1.25t + b
• August: 5 therms; $13.25• January,: 38 therms; $54.50
• One way to find the y-intercept is to pick one of the two months (let’s say August) and plug in the number of therms and the charge.
G(t) = 1.25t + b
![Page 29: Finding a linear function](https://reader033.fdocuments.in/reader033/viewer/2022060202/559d06291a28ab5d698b47ad/html5/thumbnails/29.jpg)
G(t) = 1.25t + b
• August: 5 therms; $13.25• January,: 38 therms; $54.50
• One way to find the y-intercept is to pick one of the two months (let’s say August) and plug in the number of therms and the charge.
13.25 = 1.25∙5 + b
![Page 30: Finding a linear function](https://reader033.fdocuments.in/reader033/viewer/2022060202/559d06291a28ab5d698b47ad/html5/thumbnails/30.jpg)
G(t) = 1.25t + b
• August: 5 therms; $13.25• January,: 38 therms; $54.50
• One way to find the y-intercept is to pick one of the two months (let’s say August) and plug in the number of therms and the charge.
13.25 = 6.25 + b
![Page 31: Finding a linear function](https://reader033.fdocuments.in/reader033/viewer/2022060202/559d06291a28ab5d698b47ad/html5/thumbnails/31.jpg)
G(t) = 1.25t + b
• August: 5 therms; $13.25• January,: 38 therms; $54.50
• One way to find the y-intercept is to pick one of the two months (let’s say August) and plug in the number of therms and the charge.
7 = b
![Page 32: Finding a linear function](https://reader033.fdocuments.in/reader033/viewer/2022060202/559d06291a28ab5d698b47ad/html5/thumbnails/32.jpg)
G(t) = 1.25t + b
• August: 5 therms; $13.25• January,: 38 therms; $54.50
• Now we found the y-intercept:
7 = b
![Page 33: Finding a linear function](https://reader033.fdocuments.in/reader033/viewer/2022060202/559d06291a28ab5d698b47ad/html5/thumbnails/33.jpg)
G(t) = 1.25t + 7
• August: 5 therms; $13.25• January,: 38 therms; $54.50
• Now we found the y-intercept:
7 = b
![Page 34: Finding a linear function](https://reader033.fdocuments.in/reader033/viewer/2022060202/559d06291a28ab5d698b47ad/html5/thumbnails/34.jpg)
G(t) = 1.25t + 7
• August: 5 therms; $13.25• January,: 38 therms; $54.50
• So we have the formula!
![Page 35: Finding a linear function](https://reader033.fdocuments.in/reader033/viewer/2022060202/559d06291a28ab5d698b47ad/html5/thumbnails/35.jpg)
G(t) = 1.25t + 7
• August: 5 therms; $13.25• January,: 38 therms; $54.50
• So we have the formula!
G(t) = 1.25t + 7