Finding the formula of a linear function

f(x ) = mx + b

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.

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.

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.

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

G(t) = mt + b

• August: 5 therms; $13.25• January,: 38 therms; $54.50

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:

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:

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

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

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

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

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

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

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

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

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

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

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

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

G(t) = 1.25t + b

• August: 5 therms; $13.25• January,: 38 therms; $54.50

• We found the slope

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

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

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)

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

• 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

• 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

• 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

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

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

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

G(t) = 1.25t + b

• August: 5 therms; $13.25• January,: 38 therms; $54.50

• Now we found the y-intercept:

7 = b

G(t) = 1.25t + 7

• August: 5 therms; $13.25• January,: 38 therms; $54.50

• Now we found the y-intercept:

7 = b

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

• August: 5 therms; $13.25• January,: 38 therms; $54.50

• So we have the formula!

G(t) = 1.25t + 7