The picture below shows a thermometer with both Fahrenheit and Celsius temperatures: Temperature in degrees Fahrenheit; F,is a linear function of the temperature in degrees Celsius, C ROILING POINT OFWATER By looking at the picture, identify two ordered pairs 212 1 that lie on the graph of this function (Note: the 176 ordered pairs will have the form (C,F)) Find the I slope between the two points = 140 and express Fas alinear 1 function of € 101 FAHRENHEIT I00 CELSIUS FRFEZING FOINT OFWATER Using the function you found; determine the Celsius equivalent of 689 Fahrenheit: Show work and round your answer to two decimal places if needed: (If F = 68.€ = 222) There isa particular temperature; T,for which T degrees Fahrenheit = T degrees Celsius Using your above function_ as well as the equation F = C, solve for that particular temperature. Show work

### Video Transcript

Okay. Um Okay we want to ordered pairs in this form. So looking at the thermometer I see 20 Celsius is 68. Fahrenheit and 10 Celsius is 50 F. And we want to um Find the slope between those. So we'll do the change in Y 68 -50 Over change in X 20-10. So that is 18/10. If I divide by two that is 9/5. Mhm. Okay so the slope is 9/5 times are Celsius and we can see on the thermometer that the um zero Celsius is 32 F. So 32 would be our y intercept and that will equal Fahrenheit. Okay then using the function you found determine the Celsius equivalent of 68 F. So if nine fists c plus 32 is 68 Then we will subtract the 32 from both sides. 950 will equal 36. And then to get rid of the nine fish, you multiply those sides by five nines, cancel those guys out. So we do 36 times five and then divide by nine. And that is 20. And that is one of the points I picked. Okay. And then the next part we state that there is a particular temperature t for which T degrees Fahrenheit equals two degrees Celsius. Using the bell function as well as the equation ethical. See. Alright, so let's write our other Fahrenheit equation and the fact that F equals C. Solve for that particular temperature. Alright so if F. And c are equal, I can replace either one with the other. So I'll put the Fahrenheit in And I'll say one f and then subtract the 9/5 from both sides. one is 5/5 minus 9/5. That gives us -4/5. He was 32. So to get rid of the negative 4/5 should multiply both sides by negative 5/4 And that will give us fair and high equals negative. So we'll do 32 times five and then divide by four. So a negative 40°F is equal to negative 40°C.