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)?

Question

Ethan Adkins · Accepted Answer

Point-slope form of an equation for a line is
#(y-y_1) = m(x-x_1)#
for a line with slope #m# through a point #(x_1,y_1)# Slope (y)intercept form for a line is
#y=mx+b#
for a line with slope #m# and a y-intercept of #b# The given line #y=7x-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 #(1,-2)# is
#(y-(-2)) = 7(x-1)#
which you might simplify as
#y+2 = 7(x-1)#  (although this "hides" the true #y# coordinate value)

Avery Alexander · Answer

undefined The equation of a line in point-slope form is given by $y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is a point on the line, and $m$ is the slope of the line.

To find the equation of a line parallel to $y = 7x - 1$ and passing through the point $(1, -2)$, we need to use the same slope as the given line, which is $m = 7$.

Substitute the point $(1, -2)$ and the slope $m = 7$ into the point-slope form equation:

$y - (-2) = 7(x - 1)$

Simplify:

$y + 2 = 7(x - 1)$