Question

the nine points shown below represent celsius temperatures and their equivalent fahrenheit temperatures. also shown is a line that passes through the points. answer parts a and b using the graph.
a. use the coordinates of the two points identified by the labels on the graph to compute the line’s slope. express the answer as a fraction reduced to lowest terms. what does this mean about the change in fahrenheit temperature for each degree change in celsius temperature?
the slope is \\(\square\\). this means that for every \\(1^\circ\\) that celsius changes, fahrenheit changes \\(\square^\circ\\)
(type integers or simplified fractions.)

Explanation:

Step1: Recall the slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
We have two points: \((- 15,5)\) and \((0,32)\). Let \((x_1,y_1)=(-15,5)\) and \((x_2,y_2)=(0,32)\).

Step2: Substitute into the slope formula

Substitute the values into the formula: \( m=\frac{32 - 5}{0-(-15)}=\frac{27}{15} \).

Step3: Simplify the fraction

Simplify \(\frac{27}{15}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 3. So \(\frac{27\div3}{15\div3}=\frac{9}{5}\).

The slope represents the rate of change of Fahrenheit with respect to Celsius. So for every \(1^\circ\) change in Celsius, Fahrenheit changes by \(\frac{9}{5}^\circ\).

Answer:

The slope is \(\frac{9}{5}\). This means that for every \(1^\circ\) that Celsius changes, Fahrenheit changes \(\frac{9}{5}^\circ\).