Question 336230
The quicker way is to find the x and y intercepts and plot them.
To find the x-intercept, set y=0 and solve for x.
{{{3y+x=5}}}
{{{0+x=5}}}
{{{x=5}}}
(5,0)
Plot it.
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{{{drawing(300,300,-6,6,-6,6,grid(1),circle(5,0,.3),graph(300,300,-6,6,-6,6,0))}}}
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To find the y-intercept, set x=0 and solve for y.
{{{3y+x=5}}}
{{{3y+0=5}}}
{{{3y=5}}}
{{{y=5/3}}}
(0,5/3)
Plot it too.
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{{{drawing(300,300,-6,6,-6,6,grid(1),circle(0,5/3,0.3),circle(5,0,.3),graph(300,300,-6,6,-6,6,0))}}}
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Now connect the points with a line going through both of them.
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{{{drawing(300,300,-6,6,-6,6,grid(1),circle(0,5/3,0.3),circle(5,0,.3),graph(300,300,-6,6,-6,6,(5-x)/3))}}}
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The equation of the line that you found is correct,
{{{highlight(y=-(1/3)x+5/3)}}}