When the Celsius temperature is 15degrees, the corresponding Fahrenheit temperature is 59degrees. When the Celsius temperature is 75degrees, the corresponding Fahrenheit temperature is 167 degrees . Let C represent the Celsius temperature and F the Fahrenheit temperature. a. Express F as an exact linear function of C. b. Solve the equation in part a for C, thus expressing C as a function of F. c. For what temperature is FequalsC?

(a)

(b)

(c) -40 degree

Step-by-step explanation:

(a)

A linear function is of the form

Given:

Temperature in Fahrenheit is given as 'F' and in Celsius is 'C'.

So, the linear relation is of the form , where, 'm' and 'b' are real numbers.

Now, when

When

Now, plugging these values in the above equation and solving for 'm' and 'b', we have:

Now, plugging 'm' value in first equation to get 'b' value, we have:

Therefore, the equation expressed for 'F' in terms of 'C' is given as:

(b)

In order to solve for 'C', we isolate 'C' from the above equation.

Add -32 both sides. This gives,

Divide both sides by 1.8. This gives,

Therefore, the equation solved for 'C' is

(c)

Let the temperature be 'x' when F = C.

Therefore,

Therefore, at -40 degree, the temperature in Fahrenheit equals that in Celsius.

(- 1, 0 )

step-by-step explanation:

an x- intercept is where the function crosses the x- axis.

to find the x- intercept/s look for the value of x when f(x) = 0

from the given table there are 3 values of x where f(x) = 0

when x = - 1, x = 2, x = 3

the one that is listed is (- 1, 0 )