What is the slope and intercept of #-12x-4y=2#?

Question

Avery Alexander · Accepted Answer

Slope: #(-3)#
y-intercept: #-1/2# The easiest way to handle this question is to convert the given equation: #-12x-4y=2# into "slope-intercept" form: #color(white)("XXX")y=color(green)(m)x+color(blue)(b)# with slope #color(green)(m)# and y-intercept #color(blue)(b)# #-12x-4y=2# #color(white)("XXX")rarr -4y=12x+2# #color(white)("XXX")rarr y=color(green)(-3)xcolor(blue)(-1/2)# which is in slope-intercept form with slope #color(green)(""(-3))# and y-intercept #color(blue)(""(-1/2))# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ If the x-intercept is also required, it can be found by setting #y=0# in the original equation and solving for #x# #color(white)("XXX")-12x-4(0)=2# #color(white)("XXX")rarr x=-1/6#

Abigail Allen · Answer

undefined The slope-intercept form of a linear equation is $y = mx + b$, where $m$ represents the slope and $b$ represents the y-intercept.

Given the equation $-12x - 4y = 2$, first, solve for $y$ to isolate it:

1. Subtract $-12x$ from both sides: $-4y = 12x + 2$.
2. Divide both sides by $-4$ to solve for $y$: $y = -3x - \frac{1}{2}$.

Comparing this equation to the slope-intercept form, we see that the slope $m$ is $-3$ and the y-intercept $b$ is $-\frac{1}{2}$. Therefore, the slope is $-3$ and the y-intercept is $-\frac{1}{2}$.