How do you find the slope of a line parallel to #-3y-5y=6#?

1 Answer
Mar 29, 2017

Answer:

See the solution below:

Assuming the equation is NOT #-3color(red)(x) - 5y = 6#

Explanation:

We can rewrite this as:

#(-3 - 5)y = 6#

#-8y = 6#

#(-8y)/color(red)(-8) = 6/color(red)(-8)#

#(color(red)(cancel(color(black)(-8)))y)/cancel(color(red)(-8)) = -6/8#

#y = -6/8#

#y = color(red)(a)# where #color(red)(a)# is any number is a horizontal line. A horizontal like has slope #m = 0#. Therefore any line parallel to #y = -6/8# will by definition have the same slope of #m = 0#

If the problem IS for equation #-3x - 5y = 6# we can multiply each side of the equation to put this into Standard Form. The standard form of a linear equation is: #color(red)(A)x + color(blue)(B)y = color(green)(C)#

Where, if at all possible, #color(red)(A)#, #color(blue)(B)#, and #color(green)(C)#are integers, and A is non-negative, and, A, B, and C have no common factors other than 1

#-1(-3x - 5y) = -1 * 6#

#(-1 * -3x) + (-1 * -5y) = -6#

#color(red)(3)x + color(blue)(5)y = color(green)(-6)#

The slope of an equation in standard form is: #m = -color(red)(A)/color(blue)(B)#

Therefore, substituting the values from the equation gives a slope of:

#m = -color(red)(3)/color(blue)(5)#

Because parallel lines have the same slope, any line parallel to this line will have a slope of #m = -3/5#