Slopes of secant lines passing through P(15, 520) and Q(t, V(t)) can be calculated using V(t) - 520 t - 15 Msec = We begin by calculating the slope whent = 5. V(5) – 520 5-15 msec = - 520 5-15 -.5 X (rounded to the nearest tenth)

Calculus: Early Transcendentals
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Chapter1: Functions And Models
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### Calculating the Slope of Secant Lines

#### Determining the Slope of Secant Lines Passing Through Two Points

To find the slopes of secant lines passing through the points \( P(15, 520) \) and \( Q(t, V(t)) \), we use the following formula:

\[ m_{\text{sec}} = \frac{V(t) - 520}{t - 15} \]

#### Example Calculation

Let's calculate the slope when \( t = 5 \):

\[ m_{\text{sec}} = \frac{V(5) - 520}{5 - 15} \]

Given that \( V(5) = 5 \):

\[ m_{\text{sec}} = \frac{5 - 520}{5 - 15} \]

\[ m_{\text{sec}} = \frac{5 - 520}{5 - 15} \]

\[ m_{\text{sec}} = \frac{-515}{-10} \]

\[ m_{\text{sec}} = 51.5 \]

Here, the final result is rounded to the nearest tenth, which is \( -0.5 \).

> **Note:** Pay careful attention to sign changes during calculation. The correct use of negative signs influences the final result. Ensure calculations are accurately performed to avoid errors.
Transcribed Image Text:### Calculating the Slope of Secant Lines #### Determining the Slope of Secant Lines Passing Through Two Points To find the slopes of secant lines passing through the points \( P(15, 520) \) and \( Q(t, V(t)) \), we use the following formula: \[ m_{\text{sec}} = \frac{V(t) - 520}{t - 15} \] #### Example Calculation Let's calculate the slope when \( t = 5 \): \[ m_{\text{sec}} = \frac{V(5) - 520}{5 - 15} \] Given that \( V(5) = 5 \): \[ m_{\text{sec}} = \frac{5 - 520}{5 - 15} \] \[ m_{\text{sec}} = \frac{5 - 520}{5 - 15} \] \[ m_{\text{sec}} = \frac{-515}{-10} \] \[ m_{\text{sec}} = 51.5 \] Here, the final result is rounded to the nearest tenth, which is \( -0.5 \). > **Note:** Pay careful attention to sign changes during calculation. The correct use of negative signs influences the final result. Ensure calculations are accurately performed to avoid errors.
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