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How do you graph using slope and intercept of $6 x - 3 y = - 12$ $6x - 3y = -12$ ?

1 Answer

Nov 1, 2015

$6 x - 3 y = - 12$ $6x-3y=-12$ has a slope of $2$ $2$ and a y-intercept of $4$ $4$
Starting at the y-intercept $(0, 4)$ $(0,4)$ plot points by repetitively going 1 step right and 2 steps up.

Explanation:

The y-intercept is the value of $y$ $y$ when $x = 0$ $x=0$
For $6 x - 3 y = - 12$ $6x-3y=-12$ when $x = 0$ $x=0$
$XXX 6 (0) - 3 y = - 12 \Rightarrow y = 4$ $color(white)("XXX")6(0)-3y=-12 rArr y=4$
So the y-intercept is at $(0, 4)$ $(0,4)$

The slope for an equation in the form
$XXX A x + B y = C$ $color(white)("XXX")Ax+By=C$
is $m = - \frac{A}{B}$ $m=-A/B$
So the slope of
$XXX 6 x - 3 y = - 12$ $color(white)("XXX")6x-3y=-12$
is $m = - \frac{6}{- 3} = 2$ $m= -6/(-3) = 2$

A slope of $2$ $2$ means that for every steep in the positive $x$ $x$ direction the value of $y$ $y$ must increase by $2$ $2$

graph{(6x-3y+12)(x^2+(y-4)^2-0.01)((x-1)^2+(y-6)^2-0.01)((x-2)^2+(y-8)^2-0.01)=0 [-2.505, 17.495, -0.6, 9.4]}

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