The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have the equations in the standard form. Convert to the slope-intercept form:
[tex]3x+y=-10[/tex] subtract 3x from both sides
[tex]y=-3x-10[/tex]
[tex]-x+3y=0[/tex] add x to both sides
[tex]3y=x[/tex] divide both sides by 3
[tex]y=\dfrac{1}{3}x[/tex]
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We need only two points to plot a graph of each function.
[tex]y=-3x-10[/tex]
for x = 0 and for x = -3:
[tex]y=-3(0)-10=0-10=-10\to(0,\ -10)\\\\y=-3(-3)-10=9-10=-1\to(-3,\ -1)[/tex]
[tex]y=\dfrac{1}{3}x[/tex]
for x = 0 and for x = -3:
[tex]y=\dfrac{1}{3}(0)=0\to(0,\ 0)\\\\y=\dfrac{1}{3}(-3)=-1\to(-3,\ -1)[/tex]
Look at the picture.
