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
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
To compare the Fahrenheit and Celsius scales, we can examine the relationship between the two using the given examples:
Temperature A:
- 50 degrees Celsius
- 122 degrees Fahrenheit
Temperature B:
- 100 degrees Celsius
- 212 degrees Fahrenheit
To determine the relationship between the Fahrenheit and Celsius scales, we can create a linear equation in the form of y = mx + b, where y represents the Fahrenheit temperature and x represents the Celsius temperature.
We can use the formula to convert Celsius to Fahrenheit:
F = (9/5)C + 32
Using the example of Temperature A (50 degrees Celsius and 122 degrees Fahrenheit), we can substitute the values into the equation:
122 = (9/5) * 50 + 32
Simplifying the equation gives:
122 = 90 + 32
122 = 122
The equation holds true for Temperature A.
Now, using the example of Temperature B (100 degrees Celsius and 212 degrees Fahrenheit), we can substitute the values into the equation:
212 = (9/5) * 100 + 32
Simplifying the equation gives:
212 = 180 + 32
212 = 212
The equation also holds true for Temperature B.
From these examples, we can conclude that the relationship between the Fahrenheit and Celsius scales is a linear one, and the equation of the line in slope-intercept form is:
F = (9/5)C + 32
To compare the Fahrenheit and Celsius scales, we can examine the relationship between corresponding temperature values. We have two examples given:
Temperature A:
- Celsius: 50 degrees
- Fahrenheit: 122 degrees
Temperature B:
- Celsius: 100 degrees
- Fahrenheit: 212 degrees
To graph the relationship between these scales, we can plot these two points on a graph. The Celsius values will be plotted on the x-axis, and the Fahrenheit values on the y-axis.
Plotting Temperature A (50 degrees Celsius, 122 degrees Fahrenheit), we get the point (50, 122).
Plotting Temperature B (100 degrees Celsius, 212 degrees Fahrenheit), we get the point (100, 212).
To find the equation of the line that represents this relationship, we can use the slope-intercept form of a linear equation: y = mx + b.
Let's find the slope (m) first. The slope is given by the formula: m = (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are the coordinates of two points on the line.
Using the coordinates (50, 122) and (100, 212), the slope is:
m = (212 - 122) / (100 - 50) = 90 / 50 = 9 / 5 = 1.8
Now, let's find the y-intercept (b) by substituting one of the points into the equation:
122 = (1.8)(50) + b
122 = 90 + b
b = 122 - 90
b = 32
Therefore, the equation of the line representing the relationship between Fahrenheit (y) and Celsius (x) in slope-intercept form is:
y = 1.8x + 32
This equation models the conversion between Fahrenheit and Celsius scales.