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Chapter 10: Problem 52

Calculate the slope given the following data. $$\begin{array}{ll}{y_{2}=63.7 \mathrm{mL}} & {x_{2}=5 \mathrm{s}} \\\ {y_{1}=43.5 \mathrm{mL}} & {x_{1}=2 \mathrm{s}}\end{array}$$

Short Answer

Expert verified
The slope of the line is \( \frac{20.2mL}{3s} \) or approximately 6.73 mL/s.

Step by step solution

01

Identify the Given Points

The given points are: \((x_1, y_1) = (2s, 43.5mL)\) and \((x_2, y_2) = (5s, 63.7mL)\). When a problem provides coordinates like these, they typically represent the values of 'x' and 'y' at two different points. The 'x' values represent time in seconds and the 'y' values represent volume in milliliters.
02

Substitute the Given Points into the Slope Formula

Substitute \((x_1, y_1)\) and \((x_2, y_2)\) into the slope formula \(m=\frac{y_2-y_1}{x_2-x_1}\). So, \(m=\frac{63.7mL- 43.5mL}{5s -2s}\).
03

Calculate the Slope

Following the rules of operations, begin by subtracting the 'y' values and the 'x' values in the numerator and the denominator respectively. So, \(m=\frac{63.7mL - 43.5mL}{5s -2s} = \frac{20.2mL}{3s}\).

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