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. graph with (0,32) and (10,50) 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 \\(\square\\). (type an equation using c and f as the variables. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Identify slope and y-intercept

From part a, slope \( m = \frac{9}{5} \). The y-intercept \( b \) is from the point \((0, 32)\), so \( b = 32 \).

Step2: Substitute into slope-intercept form

The slope-intercept form is \( y = mx + b \). Here, \( y \) is \( F \) (Fahrenheit) and \( x \) is \( C \) (Celsius). Substitute \( m = \frac{9}{5} \) and \( b = 32 \):
\( F = \frac{9}{5}C + 32 \)

Answer:

\( F = \frac{9}{5}C + 32 \)