# Write an equation in slope-intercept form for an equation of a line perpendicular to y=−3x+1 and that intersects at point (1,2/3)

Write an equation in slope-intercept form for an equation of a line perpendicular to y=−3x+1 and that intersects at point $\left(1,\frac{2}{3}\right)$
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Layne Murillo
The slope of this line is −3. Slope of a line perpendicular to it it $\frac{1}{3}$.
Because ${m}_{1}\cdot {m}_{2}=-1$ where ${m}_{1}$ and ${m}_{2}$ are the slope of perpendicular lines
Now, the equation of the line is $y=\frac{x}{3}+c$
To find c, put a point which in this case is $\left(1,\frac{2}{3}\right)$
$\frac{2}{3}=\frac{1}{3}+c$ $⇒$ We get that $c=\frac{1}{3}$
So required equation is $y=\frac{x}{3}+\frac{1}{3}$ or 3y=x+1