# How do you write the equation of a line in point slope form that is parallel to y=7x-1 and goes through (1,-2)?

May 7, 2015

Point-slope form of an equation for a line is
$\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)$
for a line with slope $m$ through a point $\left({x}_{1} , {y}_{1}\right)$

Slope (y)intercept form for a line is
$y = m x + b$
for a line with slope $m$ and a y-intercept of $b$

The given line $y = 7 x - 1$ is in slope-intercept form with a slope of $m = 7$

Any line parallel to this will also have a slope of $m = 7$

Point-slope form of an equation for a line with $m = 7$ through the point $\left(1 , - 2\right)$ is
$\left(y - \left(- 2\right)\right) = 7 \left(x - 1\right)$
which you might simplify as
$y + 2 = 7 \left(x - 1\right)$ (although this "hides" the true $y$ coordinate value)