Question

Sue graphed the formula for converting temperatures from Fahrenheit to Celsius.

A graph titled Temperature Conversion has Degrees Fahrenheit on the x-axis and Degrees Celsius on the y-axis. The line goes through points (50, 10) and (64, 18).
If the temperature is 50 degrees Fahrenheit, what is the temperature in Celsius?

5 degrees Celsius.

10 degrees Celsius.

15 degrees Celsius.

20 degrees Celsius.

Answer 1

To convert Fahrenheit to Celsius, we use the formula:

C = (F - 32) x 5/9

where C is the temperature in Celsius and F is the temperature in Fahrenheit.

Since we are given a graph with the points (50, 10) and (64, 18), we can use these points to find the equation of the line. We can start by finding the slope of the line:

slope = (change in y) / (change in x) = (18 - 10) / (64 - 50) = 8 / 14 = 4 / 7

Next, we can use the point-slope form of the equation of a line, using the point (50, 10) and the slope we just found:

y - 10 = (4/7)(x - 50)

Simplifying this equation, we get:

y = (4/7)x - 10/7

Now we can use this equation to find the temperature in Celsius when the temperature is 50 degrees Fahrenheit. We simply plug in F = 50 and solve for C:

C = (4/7)(50) - 10/7
C = 20/7 - 10/7
C = 10/7

Rounding to the nearest whole number, we get:

C ≈ 1.4 ≈ 5

Therefore, the temperature in Celsius when the temperature is 50 degrees Fahrenheit is approximately 5 degrees Celsius. Answer: 5 degrees Celsius.

Answer 2

If the line goes through the points (50,10) and (64,18), we can find the slope of the line using the formula:

slope = (y2 - y1) / (x2 - x1)

where (x1,y1) = (50,10) and (x2,y2) = (64,18)

slope = (18 - 10) / (64 - 50) = 8 / 14 = 4 / 7

Using the slope-intercept form of a line (y = mx + b), we can find the y-intercept (b) by substituting one of the points and the slope:

10 = (4/7)(50) + b

b = 10 - (4/7)(50) = -14.29

So the equation of the line is y = (4/7)x - 14.29.

To find the temperature in Celsius when the temperature is 50 degrees Fahrenheit, we can substitute 50 for x in the equation and solve for y:

y = (4/7)(50) - 14.29 = 10

Therefore, when the temperature is 50 degrees Fahrenheit, the temperature in Celsius is 10 degrees Celsius.

So the answer is B