Question

you are trying to compare the fahrenheit and celsius scals and you have two example: Temperature A is 50 degrees celsius and 122 degrees fahrenheit. temperature b is 100 degrees celsius and 212 degrees fahrenheit. what graph models the relationship between the fahrenheit and celsius scales? what is an equation of the line in slope intercept form

Answer 1

To compare the relationship between the Fahrenheit and Celsius scales, we can create a scatter plot graph with Fahrenheit on the x-axis and Celsius on the y-axis.

- For Temperature A:
- Fahrenheit (x) = 122
- Celsius (y) = 50

Plot the point (122, 50) on the graph.

- For Temperature B:
- Fahrenheit (x) = 212
- Celsius (y) = 100

Plot the point (212, 100) on the graph.

By connecting these two points, we can draw a straight line.

To find the equation of the line in slope-intercept form (y = mx + b), we can determine the slope (m) and the y-intercept (b) using the two points we plotted on the graph.

Slope (m) can be calculated using the formula: m = (change in y) / (change in x)

m = (100 - 50) / (212 - 122)
= 50 / 90
= 5/9

Now, to find the y-intercept (b), we can use the slope-intercept form by substituting one of the points, e.g. (122, 50):
50 = (5/9)(122) + b

Solving for b:
50 = 610/9 + b
50 - 610/9 = b
450/9 - 610/9 = b
-160/9 = b

Therefore, the equation of the line in slope-intercept form is:
y = (5/9)x - 160/9