Question

The relationship between the Fahrenheit and Celsius temperature scales is given by the linear function\({\bf{f = }}\frac{{\bf{9}}}{{\bf{5}}}{\bf{c + 32}}{\bf{.}}\)

(a) Sketch a graph of this function

(b)What is the slope of the graph and what does it represent? What is the

F-intercept and what does it represent?

Short answer

(a) The graph is given below.

(b) The slope represents the Fahrenheit temperature corresponding to a Celsius temperature of\({0^ \circ }C\).

Step-by-step solution

Given data

The relationship between the Fahrenheit and Celsius temperature scales is\(f = \frac{9}{5}c + 32\)

(a) The graph is given below\(\)\(\)

The graph of the function the given function is given below;

(b) Determine the slope of the graph and what does it represent

On comparing with the equation\(y = mx + c\), we get\(m = \frac{9}{5}\).

Therefore, the slope of the graph is\(\frac{9}{5}\), which means that for each increase of 1 degree for C, F increase\(\frac{9}{5}\)degrees.

From the graph, it can be found that F-intercept is 32, which is the Fahrenheit temperature corresponds to a Celsius temperature of\({0^ \circ }C\).