There's two parts to this question pls read it all

Question

There's two parts to this question.                                         A temperature of 0*C equals 32*F, and 25*C equals 77*F.           A. Find a liner equation using (C,F) for these data points.         B. Use this equation to find the Fahrenheit temperature for  40*C.

Answer 1

The 0 on Celsius is equivalent to 32 on Fahrenheit.

The 25 on Celsius is equivalent to 77 on Fahrenheit.

For every "C" on Celsius there is an "F" on Fahrenheit.

To develope a formula to calculate F for a given C, we should equate the segments ratios on both sides.

If 40 on Celsius then

Therefore a temperature of 40^oC equals 104^oF.

Answer 2

Write the temperature in Celsius as x - coordinate and the temperature in Fahrenheit as y - coordinate.

Treat the data as ordered pairs (C, F) and the data points are (0, 32) and (25, 77).

(A) find the linear equation using (C, F) for these data points as follows :

The point - slope from of line equation is y - y₁ = m(x - x₁), m is slope and (x₁, y₁) is point.

The points are (x₁, y₁) = (0, 32) and (x₂, y₂) = (25, 77).

Slope m = (y₂ - y₁)/(x₂ - x₁) = (77 - 32)/(25 - 0) = 45/25 = 9/5.

To write the line equation, we can use either of the two given points.

Consider the point (x₁, y₁) = (0, 32).

Substitute m = 9/5 and (x₁, y₁) = (0, 32) in point-slope form or y - y₁ = m(x - x₁).

y - (32) = (9/5)[ x - (0) ]

y = (9/5)x + 32.

(B) Find the Fahrenheit temperature for  40℃ as follows :

Substitute the value of x = 40 in the equation y = (9/5)x + 32.

y = (9/5)(40) + 32

y = (9)(8) + 32

y = 72 + 32

y = 104.

The Fahrenheit temperature for  40℃ is 104℉.