Question

which equation represents a line which is parallel to the line 6x - 5y = 5? answer y = 6/5x - 2 y = -5/6x + 1 y = 5/6x + 3 y = -6/5x + 6

Explanation:

Step1: Rewrite the given line in slope - intercept form

First, rewrite $6x - 5y=5$ as $y = mx + b$ form.
\[

$$\begin{align*} -5y&=-6x + 5\\ y&=\frac{6}{5}x-1 \end{align*}$$

\]
The slope of the line $6x - 5y = 5$ is $m=\frac{6}{5}$.

Step2: Identify the parallel line

Parallel lines have the same slope. The slope - intercept form of a line is $y=mx + b$, where $m$ is the slope. We need to find the equation with $m = \frac{6}{5}$.
The equation $y=\frac{6}{5}x-2$ has a slope of $\frac{6}{5}$.

Answer:

$y=\frac{6}{5}x - 2$