Question

1. you be the teacher your friend finds the slope of the line shown. is your friend correct? explain your reasoning.

the image shows a coordinate grid with a line passing through points (2, 3) and (4, 1). the friends calculation is: ( m = \frac{3 - 1}{4 - 2} = \frac{2}{2} = 1 )

Explanation:

Step1: Recall slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify coordinates

Points are \((2, 3)\) (so \( x_1 = 2, y_1 = 3 \)) and \((4, 1)\) (so \( x_2 = 4, y_2 = 1 \)).

Step3: Apply formula correctly

Substitute into slope formula: \( m=\frac{1 - 3}{4 - 2}=\frac{-2}{2}=-1 \).

Step4: Analyze friend's mistake

Friend used \( \frac{3 - 1}{4 - 2} \), which swaps \( y_2 - y_1 \) (used \( y_1 - y_2 \) instead of \( y_2 - y_1 \) or vice - versa, but also the order of subtraction should be consistent for \( y \) and \( x \)). So friend's calculation is wrong.

Answer:

Your friend is not correct. The correct slope calculation is \( m=\frac{1 - 3}{4 - 2}=\frac{-2}{2}=-1 \), but your friend incorrectly calculated the numerator as \( 3 - 1 \) instead of \( 1 - 3 \) (or used inconsistent subtraction order for \( y \)-values), leading to an incorrect slope of \( 1 \) instead of \( - 1 \).