Question

Find the slope of the line passing through the pair of points. \((1,-2)\) and \((2,4)\)

Short answer

The slope of the line passing through the points \((1,-2)\) and \((2,4)\) is \(6\).

Step-by-step solution

Identify the coordinates of both points

The points are given as \((1,-2)\) and \((2,4)\). Assign them to variables: Point A: \(x1 = 1\), \(y1 = -2\) Point B: \(x2 = 2\), \(y2 = 4\)

Apply the slope formula

Using the slope formula, substitute these values: Slope = \(\frac{y2 - y1}{x2 - x1} = \frac{4 - (-2)}{2 - 1}\)

Simplify the equation

Now, perform the arithmetic: Slope = \(\frac{4 + 2}{2 - 1} = \frac{6}{1}\)

Find the slope

Simplify the fraction, the slope is: Slope = \(6\) So, the slope of the line passing through the pair of points \((1,-2)\) and \((2,4)\) is \(6\).