The following questions use the graph to the left which represents the temperature of an oven over time. 300 200 100 4. Write the equation for the line. Temperature in Fahrenheit
The following questions use the graph to the left which represents the temperature of an oven over time. 300 200 100 4. Write the equation for the line. Temperature in Fahrenheit
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
![**Graph Analysis and Equation Derivation**
The following questions use the graph to the left, which represents the temperature of an oven over time.
**Graph Description:**
- **Axes:** The graph has two axes.
- The horizontal axis (x-axis) represents the time passed in minutes.
- The vertical axis (y-axis) represents the temperature in Fahrenheit.
- **Scale:**
- The x-axis is scaled to show intervals of 2 minutes, ranging from 0 to 4 minutes.
- The y-axis is scaled to show intervals of 100 degrees Fahrenheit, ranging from 0°F to 300°F.
- **Data Representation:**
- The graph shows a straight line in red, which suggests a linear relationship between time and temperature.
- The initial point (0 minutes, 0°F) indicates the initial condition before heating starts.
- The line passes through points like (1 minute, 100°F), (2 minutes, 200°F), (3 minutes, 300°F).
**Question:**
4. Write the equation for the line.
**Solution:**
To find the equation of the line, we will determine its slope and y-intercept.
1. **Slope (m):**
- The slope \(m\) of a line is given by the formula:
\[
m = \frac{\Delta y}{\Delta x}
\]
- Using two points on the line: (1, 100) and (2, 200):
\[
m = \frac{200 - 100}{2 - 1} = \frac{100}{1} = 100
\]
2. **Y-intercept (b):**
- The line passes through the origin (0, 0), so the y-intercept \(b\) is 0.
Therefore, the equation of the line is:
\[
y = 100x
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Transcribed Image Text:**Graph Analysis and Equation Derivation**
The following questions use the graph to the left, which represents the temperature of an oven over time.
**Graph Description:**
- **Axes:** The graph has two axes.
- The horizontal axis (x-axis) represents the time passed in minutes.
- The vertical axis (y-axis) represents the temperature in Fahrenheit.
- **Scale:**
- The x-axis is scaled to show intervals of 2 minutes, ranging from 0 to 4 minutes.
- The y-axis is scaled to show intervals of 100 degrees Fahrenheit, ranging from 0°F to 300°F.
- **Data Representation:**
- The graph shows a straight line in red, which suggests a linear relationship between time and temperature.
- The initial point (0 minutes, 0°F) indicates the initial condition before heating starts.
- The line passes through points like (1 minute, 100°F), (2 minutes, 200°F), (3 minutes, 300°F).
**Question:**
4. Write the equation for the line.
**Solution:**
To find the equation of the line, we will determine its slope and y-intercept.
1. **Slope (m):**
- The slope \(m\) of a line is given by the formula:
\[
m = \frac{\Delta y}{\Delta x}
\]
- Using two points on the line: (1, 100) and (2, 200):
\[
m = \frac{200 - 100}{2 - 1} = \frac{100}{1} = 100
\]
2. **Y-intercept (b):**
- The line passes through the origin (0, 0), so the y-intercept \(b\) is 0.
Therefore, the equation of the line is:
\[
y = 100x
\]
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