Download the App!
Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.
Question
Answered step-by-step
The relationship between the Fahrenheit $ (F) $ and Celsius $ (C) $ temperature scales is given by the linear function $ F = \frac{9}{5} C + 32 $.
(a) Sketch a graph of this function.(b) What is the slope of the graph and what does it represent? What is the F-intercept and what does it represent?
Video Answer
Solved by verified expert
This problem has been solved!
Try Numerade free for 7 days
Like
Report
Official textbook answer
Video by Heather Zimmers
Numerade Educator
This textbook answer is only visible when subscribed! Please subscribe to view the answer
02:07
Jeffrey Payo
Calculus 1 / AB
Calculus 2 / BC
Calculus 3
Chapter 1
Functions and Models
Section 2
Mathematical Models: A Catalog of Essential Functions
Functions
Integration Techniques
Partial Derivatives
Functions of Several Variables
Johns Hopkins University
Missouri State University
Campbell University
Boston College
Lectures
04:31
A multivariate function is a function whose value depends on several variables. In contrast, a univariate function is a function whose value depends on only one variable. A multivariate function is also called a multivariate expression, a multivariate polynomial, a multivariate series, or a multivariate function of several variables.
12:15
In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.
02:22
The relationship between t…
02:08
03:02
01:04
02:32
01:09
01:05
01:25
Temperature Scales The rel…
01:07
The graph of Fahrenheit te…
03:27
04:26
The equation $F=\frac{9}{5…
01:12
The equation $C=\frac{5}{9…
all right. So here we have the function, which represents the temperature and degrees Celsius related to the temperature in degrees Fahrenheit Fahrenheit as a function of Celsius, and we want to sketch the graph of it. So I'm going to start by finding a couple points that would be on the graph, and then we'll draw a line through them. So if the temperature in degrees Celsius was zero, we would have 9/5 time zero plus 32. So that would be 32 F. And I'm going to choose a convenient number for C as a second point. I'm going to choose C equals 25 because it's easy to multiply by 9/5. And when we multiply 25 by 9/5 we get 45 plus 32 is 77. Okay, so we could plot these two points 0 32 and 25 77 and then we can draw the line through these points. And that represents the relationship between the two temperature scales in Part B. We want to talk about the slope. So what's the slope and what does it represent? When you look at the equation, you can see that the slope is 9/5 and if you think about the units on slope, the slope is changing. Why over change in X. So the units on why were degrees Fahrenheit and the units on on X or C? In this case, we're degrees Celsius, and so the slope is showing you the change in degrees Fahrenheit for a change in degree Celsius. So it's telling us that it would go up 9 F for every five degrees it goes up Celsius, so goes up 9 F for every five degree Celsius rise. Now, how about the y intercept or in this case will call it the F intercept, since our Y axis is known as the F axis in this problem. So the point where the graph intersects the Y axis is the 0.0.0 32 and that would be the point where it is zero degrees Celsius. So when it zero degrees Celsius, it's 32 F. Zero degree Celsius is 32 F, and we think of that as the temperature of freezing for water. That's the water's freezing temperature
View More Answers From This Book
Find Another Textbook
