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 lines 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 $\frac{9}{5}$. this means that for every $1^circ$ that celsius changes, fahrenheit changes $\frac{9}{5}^circ$.
(type integers or simplified fractions.)
b. use the slope-intercept form of the equation of a line, $y = mx + b$, the slope from part a, and the y-intercept shown by the graph to derive the formula used to convert from celsius to fahrenheit.
the formula is
(type an equation using c and f as the variables. use integers or fractions for any

Explanation:

Part b Solution:

Step 1: Recall slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. In the context of converting Celsius ($C$) to Fahrenheit ($F$), we can think of $F$ as the dependent variable (like $y$) and $C$ as the independent variable (like $x$).

We know from part (a) that the slope $m=\frac{9}{5}$. We also know from the point $(0,32)$ (when $C = 0$, $F=32$) that the y - intercept $b = 32$.

Step 2: Substitute into the slope - intercept form

Substitute $m=\frac{9}{5}$ and $b = 32$ into the equation $y=mx + b$. Replacing $y$ with $F$ and $x$ with $C$, we get:

$F=\frac{9}{5}C+32$

Answer:

The formula is $F=\frac{9}{5}C + 32$