Question

Graph 3x+y=-10 -x+3y=0

Answer 1

The slope-intercept form of an equation of a line:

$y=mx+b$

m - slope

b - y-intercept

We have the equations in the standard form. Convert to the slope-intercept form:

$3x+y=-10$            subtract 3x from both sides

$y=-3x-10$

$-x+3y=0$             add x to both sides

$3y=x$             divide both sides by 3

$y=\dfrac{1}{3}x$

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We need only two points to plot a graph of each function.

$y=-3x-10$

for x = 0 and for x = -3:

$y=-3(0)-10=0-10=-10\to(0,\ -10)\\\\y=-3(-3)-10=9-10=-1\to(-3,\ -1)$

$y=\dfrac{1}{3}x$

for x = 0 and for x = -3:

$y=\dfrac{1}{3}(0)=0\to(0,\ 0)\\\\y=\dfrac{1}{3}(-3)=-1\to(-3,\ -1)$

Look at the picture.