Question

1. find the slope of the line that passes through the points (7, -5) and (-1, -3).

a. 4
b. \\(\frac{1}{4}\\)
c. -4
d. \\(-\frac{1}{4}\\)

1. if another line is perpendicular to the line

Explanation:

Step1: Recall the slope formula

The slope \( m \) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify the coordinates

Let \((x_1, y_1)=(7, - 5)\) and \((x_2, y_2)=(-1, - 3)\).

Step3: Substitute into the formula

Substitute the values into the slope formula: \( m=\frac{-3-(-5)}{-1 - 7}=\frac{-3 + 5}{-8}=\frac{2}{-8}=-\frac{1}{4} \)? Wait, no, wait: \(-3-(-5)=-3 + 5 = 2\), and \(-1-7=-8\), so \( m=\frac{2}{-8}=-\frac{1}{4}\)? Wait, no, wait, let's check again. Wait, \( y_2 - y_1=-3-(-5)=-3 + 5 = 2\), \( x_2 - x_1=-1 - 7=-8\), so \( m=\frac{2}{-8}=-\frac{1}{4}\)? Wait, but let's check the calculation again. Wait, \( -3-(-5)=2\), \( -1 - 7=-8\), so \( \frac{2}{-8}=-\frac{1}{4}\). Wait, but let's see the options. Option D is \(-\frac{1}{4}\). Wait, but let's re - calculate:

Wait, the slope formula is \( m=\frac{y_2 - y_1}{x_2 - x_1}\). So \( y_1=-5\), \( y_2=-3\), \( x_1 = 7\), \( x_2=-1\).

So \( y_2 - y_1=-3-(-5)=-3 + 5 = 2\)

\( x_2 - x_1=-1 - 7=-8\)

So \( m=\frac{2}{-8}=-\frac{1}{4}\)

Answer:

D. \(-\frac{1}{4}\)