Question

find the slope of the line that passes through: (6,7) and (4,2) -1/2 2/5 -5/2 5/2

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 points

Let \((x_1, y_1)=(6, 7)\) and \((x_2, y_2)=(4, 2)\).

Step3: Substitute into formula

Substitute values: \( m=\frac{2 - 7}{4 - 6}=\frac{-5}{-2}=\frac{5}{2} \). Wait, no—wait, \( 2 - 7=-5 \), \( 4 - 6=-2 \), so \( \frac{-5}{-2}=\frac{5}{2} \)? Wait, no, wait: \( y_2 - y_1 = 2 - 7=-5 \), \( x_2 - x_1 = 4 - 6=-2 \), so \( \frac{-5}{-2}=\frac{5}{2} \). Wait, but let me check again. Wait, maybe I mixed up? Wait, slope formula is \( \frac{y_2 - y_1}{x_2 - x_1} \) or \( \frac{y_1 - y_2}{x_1 - x_2} \), both give same result. Let's do \( \frac{7 - 2}{6 - 4}=\frac{5}{2} \). Yes, that's correct. So the slope is \( \frac{5}{2} \). Wait, but let's check the options. The fourth option is \( 5/2 \). Wait, but wait, did I make a mistake? Wait, no: (6,7) and (4,2). So change in y: 7 - 2 = 5, change in x: 6 - 4 = 2. So slope is 5/2. So the correct option is the fourth one, \( 5/2 \). Wait, but let me check again. Wait, 2 - 7 is -5, 4 - 6 is -2, so -5/-2 is 5/2. Yes. So the slope is 5/2.

Answer:

D. \( 5/2 \) (assuming the options are labeled as A: -1/2, B: 2/5, C: -5/2, D: 5/2)