Problem 3 - Introductory and Intermediate Algebra for College Students 4th

Question

Find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. $$(-2,1) \text { and }(2,2)$$

Step-by-Step Solution

Answer

The slope of the line is \(1/4\) and the line rises.

Step 1: Identify the given points and apply the slope formula

The given points are (-2,1) and (2,2). To calculate the slope, use the formula \(m = (y_2 - y_1) / (x_2 - x_1)\). The coordinates of the first point are \((-2,1) = (x_1,y_1)\) and the second point are \((2,2) = (x_2,y_2)\).

Step 2: Substitute the values into the slope formula

Now, substitute the values of the coordinates into the slope formula. So \(m = (2 - 1) / (2 - -2)\).

Step 3: Solve the expression

Simplify the expression obtain: \(m = 1/4\).

Step 4: Interpret the Slope

Since the slope is positive, this means that the line rises.