What is the equation of the line passing through (2, –3) and parallel to the line #y = –6x – 1# in standard form?

Question

Savannah Anderson · Accepted Answer

The answer is #6x+y-9=0# You start by noting that the function you are looking for can be written as #y=-6x+c# where #c in RR# because two parallel lines have the same "x" coeficients.
Next you have to calculate #c# using the fact that the line passes through #(2,-3)#
After solving the equation #-3=-6*2+c#
#-3=-12+c#
#c=9#
So the line has the  equation #y=-6x+9#
To change it to the standard form you just have to move #-6x+9# to the left side to leave #0# on the right side, so you finally get:
#6x+y-9=0#

Eli Assouline · Answer

undefined To find the equation of the line passing through the point (2, –3) and parallel to the line $ y = -6x - 1 $ in standard form $ Ax + By = C $, first determine the slope of the given line, which is -6. Parallel lines have the same slope. Then, use the point-slope form $ y - y_1 = m(x - x_1) $ with the given point (2, –3). Substitute the slope and the coordinates into the equation to find the equation in point-slope form. After that, convert it into standard form. The resulting equation will be $ 6x + y = 9 $.