The problem asks us to plot a graph representing the conversion between Celsius (°C) and Fahrenheit (°F) temperatures, given the freezing point of water ($0°C = 32°F$) and the boiling point of water ($100°C = 212°F$). We are told the graph is a straight line.

1. Problem Description

The problem asks us to plot a graph representing the conversion between Celsius (°C) and Fahrenheit (°F) temperatures, given the freezing point of water ($0°C = 32°F$) and the boiling point of water ($100°C = 212°F$). We are told the graph is a straight line.

2. Solution Steps

Since we know two points on the line and that it is a straight line, we can plot these points on the provided graph and draw a line through them. The two points are (0, 32) and (100, 212), where the x-coordinate represents Celsius and the y-coordinate represents Fahrenheit.

Plotting these points on the graph, we can then draw a straight line connecting the points (0, 32) and (100, 212). We can extend this line beyond these points to cover the entire graph. The graph will thus represent the conversion between Celsius and Fahrenheit temperatures.

We can find the equation of the line representing the conversion as well.

The general equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. In our case, $y$ represents Fahrenheit and $x$ represents Celsius. The slope, $m$, can be calculated as the change in Fahrenheit divided by the change in Celsius between the two known points:

$m = \frac{212 - 32}{100 - 0} = \frac{180}{100} = \frac{9}{5} = 1.8$

The y-intercept, $b$, is the value of Fahrenheit when Celsius is 0, which is given as

3

2. Therefore, $b = 32$.

So, the equation for converting Celsius to Fahrenheit is:

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

$F = 1.8C + 32$

3. Final Answer

The solution is a graph (plot a line), showing the conversion between Celcius and Fahrenheit. Plot the points (0,32) and (100,212), and draw a line through those points, extending it to fill the graph.