Question

describe the error in finding the slope of the line. m = \frac{3 - 1}{4 - 2}=\frac{2}{2}=1. the numerator and denominator should be switched. the numerator should be 4 - 3. the denominator should be 2 - 4. the fraction was simplified incorrectly. the correct slope of the line is

Explanation:

Step1: Recall slope formula

The slope formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Given points $(2,3)$ and $(4,1)$, we should have $m=\frac{1 - 3}{4 - 2}$. The error in the given work is that the denominator should be $2-4$ if we consider the order of subtraction as $\frac{3 - 1}{2 - 4}$ to be consistent with the slope - formula.

Step2: Calculate correct slope

$m=\frac{1 - 3}{4 - 2}=\frac{-2}{2}=-1$. Or if we write it as $\frac{3 - 1}{2 - 4}=\frac{2}{-2}=-1$.

Answer:

The denominator should be $2 - 4$.
The correct slope of the line is $-1$