Which equation best represents the relationship shown in the graph between Celsius and Fahrenheit?

Steps to Solve

1. Identify two points on the line

From the graph, we can identify two points. It looks like $(0, 32)$ and $(10, 50)$ are on the line.

2. Calculate the slope

The slope, $m$, of a line passing through the points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $$ m = \frac{y_2 - y_1}{x_2 - x_1} $$ Using the identified points $(0, 32)$ and $(10, 50)$: $$ m = \frac{50 - 32}{10 - 0} = \frac{18}{10} = \frac{9}{5} = 1.8 $$

3. Determine the y-intercept

The y-intercept, $b$, is the value of $y$ when $x = 0$. From the graph and the point $(0, 32)$, we can see that the y-intercept is 32.

4. Write the equation in slope-intercept form

The slope-intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. Substituting the values we found for $m$ and $b$: $$ y = 1.8x + 32 $$