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Chapter 1: Problem 10

Find the slope of the line that passes through the given pair of points. $$ (-a+1, b-1) \text { and }(a+1,-b) $$

Short Answer

Expert verified
The slope of the line that passes through the given pair of points \((-a+1, b-1)\) and \((a+1, -b)\) is \(m = \frac{1 - 2b}{2a}\).

Step by step solution

01

Identify the coordinates of the given points

First, let's identify the coordinates of the given points. Point 1: \((-a+1, b-1)\) - \(x_1 = -a+1\) - \(y_1 = b-1\) Point 2: \((a+1, -b)\) - \(x_2 = a+1\) - \(y_2 = -b\)
02

Use the slope formula to find the slope

Now, we will use the slope formula: $$ m = \frac{y_2 - y_1}{x_2 - x_1} $$ Plugging in the coordinates of the given points into the slope formula: $$ m = \frac{-b - (b-1)}{(a+1) - (-a+1)} $$
03

Simplify the expression to find the slope

We can simplify the expression for the slope by performing the subtraction and addition operations in the numerator and denominator: $$ m = \frac{-b - b + 1}{a+1 + a - 1} $$ Next, we can combine like terms in both the numerator and denominator: $$ m = \frac{-2b + 1}{2a} $$ Thus, the slope of the line passing through these two given points is: $$ m = \frac{1 - 2b}{2a} $$

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