How do you find a standard form equation for the line with (-2,2) and is parallel to the line whose equation is 2x-3y-7=0?

Question

Nathan Axel · Accepted Answer

#2x-3y+10=0#

#2x-3y-7=0# and any line parallel to it has a slope of #color(green)(m=2/3)#
#color(white)("XXX")#We know this either because:
#color(white)("XXX")[1]color(white)("XX")#we know #Ax+By+c=0# has a slope of #color(green)(-A/B)#
#color(white)("XXX")#or
#color(white)("XXX")[2]color(white)("XX")# by converting into slope-intercept form: #y=color(green)(m)x+b#
~~~~~~~~~~~~~~~~~~~~~~~~
If a line has a slope of #color(green)(2/3)# and passes through #(color(red)(-2),color(blue)(2))#
then it has a slope-point form of
#color(white)("XXX")y-color(blue)(2)=color(green)(2/3)(x-color(red)(""(-2)))#

Simplifying
#color(white)("XXX")y=color(green)(2/3)(x+2)+2#

#color(white)("XXX")3y=(2x+4) +6#

or (in standard form)
#color(white)("XXX")2x-3y+10=0#

~~~~~~~~~~~~~~~~~~~~~~

For verification/support, here are the graphs:

Isaiah Anthony · Answer

undefined To find the standard form equation for a line parallel to $2x - 3y - 7 = 0$ and passing through the point (-2, 2), first, find the slope of the given line. The slope-intercept form of the given line is $y = \frac{2}{3}x - \frac{7}{3}$, so the slope is $\frac{2}{3}$. Since the line we want is parallel, it will have the same slope. Then, use the point-slope form of a line, $y - y_1 = m(x - x_1)$, where $m$ is the slope and $(x_1, y_1)$ is the given point. Plug in the slope and the point (-2, 2) to find the equation. Simplify it to standard form $Ax + By + C = 0$. So, the equation becomes $2x - 3y + 10 = 0$.