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

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

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Answer 1 · 2016-04-10T20:44:01

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

Explanation:

slope
Given an equation in the form $A x + B y = C$ $Ax+By=C$ the slope is $(- \frac{A}{B})$ $(-A/B)$
So $- 4 x + 2 y = 12$ $-4x+2y=12$ has a slope of $- \frac{- 4}{2} = 2$ $-(-4)/2=2$

Alternately, we could convert the given form
into "slope-intercept form": $y = m x + b$ $y=mx+b$ with slope $m$ $m$ and y-intercept $b$ $b$
$XXX - 4 x + 2 y = 12$ $color(white)("XXX")-4x+2y=12$
$XXX \to 2 y = 4 x + 12$ $color(white)("XXX")rarr 2y=4x+12$
$XXX \to y = 2 x + 6$ $color(white)("XXX")rarr y = 2x+6$

y-intercept
If we used the "slope-intercept form" (above) we already have the y-intercept: $6$ $6$ ;
otherwise we can determine the y-intercept by finding the value of $y$ $y$ when $x = 0$ $x=0$ in the given equation: $- 4 x + 2 y = 12$ $-4x+2y=12$
$XXX - 4 \times (0) + 2 y = 12$ $color(white)("XXX")-4xx(0)+2y=12$
$XXX \to y = 6$ $color(white)("XXX")rarr y=6$

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 $x$ $x$ when $y = 0$ $y=0$ in the given equation: $- 4 x + 2 y = 12$ $-4x+2y=12$
$XXX - 4 x + 2 \times (0) = 12$ $color(white)("XXX")-4x+2xx(0)=12$
$XXX \to x = - 3$ $color(white)("XXX")rarr x=-3$

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

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Explanation:

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

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Explanation:

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