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Chapter 1: Problem 34

Plot the points and find the slope of the line passing through the pair of points. $$\left(\frac{11}{2},-\frac{4}{3}\right),\left(-\frac{3}{2},-\frac{1}{3}\right)$$

Short Answer

Expert verified
The slope of the line passing through the points \( \left(\frac{11}{2}, -\frac{4}{3}\right) \) and \(\left(-\frac{3}{2}, -\frac{1}{3}\right) \) is \(0.2\).

Step by step solution

01

Identify the Coordinates

Firstly, you identify the coordinates of the two points that are given. Here, point \(A\) is \(\left(\frac{11}{2}, -\frac{4}{3}\right) = (5.5, -1.33)\) and point \(B\) is \(\left(-\frac{3}{2}, -\frac{1}{3}\right) = (-1.5, -0.33)\).
02

Calculate the Slope

The next step is to find the slope of the line passing through these two points using the formula for slope. So, we have:\[slope = \frac{y2 - y1}{x2 - x1} = \frac{-0.33-(-1.33)}{-1.5-5.5} = 0.2\]
03

Plot the Points

With the coordinates and the slope, we can now plot these on a graph. Remember, the slope of a line indicates its steepness and direction. A slope of \(0.2\) means the line increases by \(0.2\) units vertically for every unit it moves horizontally. On a graph, place point \(A\) at coordinates \( (5.5, -1.33)\) and point \(B\) at coordinates \( (-1.5, -0.33)\). Draw a line passing through these two points that has a slope of \(0.2\).

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