Which of the following figure represents the relation between Celsius and Fahrenheit temperatures?

Solution

Physics sir · 3 steps

Write C in terms of F; the graph must slope upward and cut the F-axis at 32, not at the origin.

1. Write the relation. Both scales are linear, with freezing at 0°C = 32°F and boiling at 100°C = 212°F. With C on the vertical axis and F on the horizontal axis, solve for C.

   C = 5/9(F - 32) = 5/9F - 160/9

2. Read off the shape. This is a straight line with slope +5/9, so it rises to the right. Putting C = 0 gives F = 32, a positive F-intercept. Putting F = 0 gives C = -160/9 ≈ -17.8, a negative C-intercept. So the line cannot pass through the origin.

   Option	Slope	Passes through origin?	Matches?
   (a)	positive	yes	no
   (b)	negative	no	no
   (c)	negative	yes	no
   (d)	positive	no, cuts F-axis at positive F and C-axis below 0	yes

3. So. Only (d) shows a rising line that cuts the F-axis on the positive side and the C-axis on the negative side. The answer is (d).

The idea to keep. For any two linear temperature scales, write one in terms of the other. Check the sign of the slope first, then the intercepts. A nonzero offset like 32 means the line misses the origin.

Answer from the NTA final answer key. Solution by PrepWiser.