Question

1. the slope of the line with equation $6x + 5y - 1 = 0$ is

a. $-\frac{6}{5}$
b. $-\frac{5}{6}$
c. $\frac{6}{5}$
d. $\frac{1}{5}$

Explanation:

Step1: Convert to slope - intercept form

The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope. We start with the equation \(6x+5y - 1=0\).
First, we isolate \(y\) on one side. Subtract \(6x\) and add \(1\) to both sides: \(5y=-6x + 1\).

Step2: Solve for \(y\)

Divide each term in the equation \(5y=-6x + 1\) by \(5\). We get \(y=\frac{-6x + 1}{5}\), which can be rewritten as \(y=-\frac{6}{5}x+\frac{1}{5}\).
In the slope - intercept form \(y = mx + b\), the coefficient of \(x\) is the slope. So the slope \(m =-\frac{6}{5}\).

Answer:

A. \(-\frac{6}{5}\)