What is the point-slope of the equation of the line passing through (-1,4) parallel to y=-5x+2?

Jun 23, 2015

The point-slope form of the equation of the required line is:

$y - 4 = - 5 \left(x - \left(- 1\right)\right)$

Explanation:

The equation $y = - 5 x + 2$ is in slope-intercept form, describing a line of slope $- 5$ with intercept $2$.

Any line parallel to it will have slope $- 5$.

Point slope form is:

$y - {y}_{1} = m \left(x - {x}_{1}\right)$

where $m$ is the slope and $\left({x}_{1} , {y}_{1}\right)$ is a point on the line.

So with slope $m = - 5$ and $\left({x}_{1} , {y}_{1}\right) = \left(- 1 , 4\right)$, we get:

$y - 4 = - 5 \left(x - \left(- 1\right)\right)$

The same line in slope-intercept form is:

$y = - 5 x + \left(- 1\right)$