Find the Slope of a Parallel Line 3x+y=1

$3 x + y = 1$

Rewrite in slope-intercept form.

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Subtract $3 x$ from both sides of the equation.

$y = 1 - 3 x$

Reorder $1$ and $- 3 x$ .

$y = - 3 x + 1$

Using the slope-intercept form, the slope is $- 3$ .

$m = - 3$

All lines that are parallel to $y = - 3 x + 1$ have the same slope of $- 3$ .

$m_{parallel} = - 3$