How do you find the slope and intercept of #-4x+2y=12#?

Question

Eva Adamson · Accepted Answer

Slope: #2#
y-intercept: #6#
(x-intercept: #-3#)

slope Given an equation in the form #Ax+By=C# the slope is #(-A/B)# So #-4x+2y=12# has a slope of #-(-4)/2=2# Alternately, we could convert the given form into "slope-intercept form": #y=mx+b# with slope #m# and y-intercept #b# #color(white)("XXX")-4x+2y=12# #color(white)("XXX")rarr 2y=4x+12# #color(white)("XXX")rarr y = 2x+6# y-intercept If we used the "slope-intercept form" (above) we already have the y-intercept: #6#; otherwise we can determine the y-intercept by finding the value of #y# when #x=0# in the given equation: #-4x+2y=12# #color(white)("XXX")-4xx(0)+2y=12# #color(white)("XXX")rarr y=6# x-intercept (note sometimes when "the intercept" is asked for, what is meant is only the y-intercept) The x-intercept can be determined by find the value of #x# when #y=0# in the given equation: #-4x+2y=12# #color(white)("XXX")-4x+2xx(0)=12# #color(white)("XXX")rarr x=-3#

Eli Assouline · Answer

undefined To find the slope and intercept of the equation -4x + 2y = 12, you first need to rewrite it in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

Starting with -4x + 2y = 12:
1. Add 4x to both sides to isolate the term with y: 2y = 4x + 12
2. Divide both sides by 2 to solve for y: y = 2x + 6

Comparing this equation to the slope-intercept form, we see that the slope (m) is 2, and the y-intercept (b) is 6. Therefore, the slope is 2, and the y-intercept is (0, 6).