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 9/5. this means that for every 1° that celsius changes, fahrenheit changes 9/5°. (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 numbers in the expression.)

Explanation:

Step1: Identify slope - intercept form components

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. We know from part a that $m=\frac{9}{5}$, and from the graph, the line passes through the point $(0,32)$, so the y - intercept $b = 32$.

Step2: Substitute values into the equation

Substitute $m=\frac{9}{5}$ and $b = 32$ into $y=mx + b$. Since we are using $F$ for the y - variable (Fahrenheit) and $C$ for the x - variable (Celsius), the equation becomes $F=\frac{9}{5}C+32$.

Answer:

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