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

Question

Hazel Anglin · Accepted Answer

See the solution below:

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

Nathan Axel · Answer

undefined To find the slope of a line parallel to the given line, first rewrite the equation in slope-intercept form. Then, the slope of the parallel line will be the same as the slope of the given line. So, rearrange the equation to solve for y in terms of x, and the coefficient of x will be the slope.