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what is equation of line

what is equation of line

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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what is equation of line

### Transcription for Educational Website **Graph Analysis: Calculating Velocity** The graph presents a set of data points and a fitted line that illustrates the relationship between time and the y-coordinate of a point. Below is a detailed explanation of the graph's components: **Axes:** - The x-axis represents time in seconds (s), ranging from 0 to 0.7 seconds. - The y-axis represents the y-coordinate (Y_large) in centimeters (cm), ranging from -50 cm to 100 cm. **Data Points and Line:** - The graph contains a series of black dots denoting the empirical data points collected over time. - A red line is fitted through the data points, indicating a possible trend or relationship between the variables. **Purpose:** - The instruction provided aims to guide the observer to record the slope of the red fitting line, which represents the velocity at the time \( t = 0.1 \) seconds. **Determining Velocity:** - The slope of the line on a position-time graph is indicative of the velocity of the object. - To find the slope, observe the change in the y-coordinate (ΔY_large) relative to the change in time (Δt). For instance, at \( t = 0.1 \) seconds: - Identify the y-coordinate at \( t = 0.1 \), which is approximately 0 cm. - Identify another point on the slope, for example, at \( t = 0 \) seconds, with a y-coordinate of approximately -50 cm. - Calculate the slope using the formula: \[ \text{Slope (velocity)} = \frac{Y_{2} - Y_{1}}{t_{2} - t_{1}} = \frac{0 - (-50)}{0.1 - 0} = \frac{50}{0.1} \] - The slope, or velocity, at \( t = 0.1 \) seconds is 500 cm/s. Remember, understanding the graph and the significance of its slope is crucial for analyzing and interpreting the motion of objects in physics.
Transcribed Image Text:### Transcription for Educational Website **Graph Analysis: Calculating Velocity** The graph presents a set of data points and a fitted line that illustrates the relationship between time and the y-coordinate of a point. Below is a detailed explanation of the graph's components: **Axes:** - The x-axis represents time in seconds (s), ranging from 0 to 0.7 seconds. - The y-axis represents the y-coordinate (Y_large) in centimeters (cm), ranging from -50 cm to 100 cm. **Data Points and Line:** - The graph contains a series of black dots denoting the empirical data points collected over time. - A red line is fitted through the data points, indicating a possible trend or relationship between the variables. **Purpose:** - The instruction provided aims to guide the observer to record the slope of the red fitting line, which represents the velocity at the time \( t = 0.1 \) seconds. **Determining Velocity:** - The slope of the line on a position-time graph is indicative of the velocity of the object. - To find the slope, observe the change in the y-coordinate (ΔY_large) relative to the change in time (Δt). For instance, at \( t = 0.1 \) seconds: - Identify the y-coordinate at \( t = 0.1 \), which is approximately 0 cm. - Identify another point on the slope, for example, at \( t = 0 \) seconds, with a y-coordinate of approximately -50 cm. - Calculate the slope using the formula: \[ \text{Slope (velocity)} = \frac{Y_{2} - Y_{1}}{t_{2} - t_{1}} = \frac{0 - (-50)}{0.1 - 0} = \frac{50}{0.1} \] - The slope, or velocity, at \( t = 0.1 \) seconds is 500 cm/s. Remember, understanding the graph and the significance of its slope is crucial for analyzing and interpreting the motion of objects in physics.
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