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

ormaybesaladqh
2022-10-12
Answered

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

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Layne Murillo

Answered 2022-10-13
Author has **14** answers

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 $(1,\frac{2}{3})$

$\frac{2}{3}=\frac{1}{3}+c$ $\Rightarrow$ We get that $c=\frac{1}{3}$

So required equation is $y=\frac{x}{3}+\frac{1}{3}$ or 3y=x+1

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 $(1,\frac{2}{3})$

$\frac{2}{3}=\frac{1}{3}+c$ $\Rightarrow$ We get that $c=\frac{1}{3}$

So required equation is $y=\frac{x}{3}+\frac{1}{3}$ or 3y=x+1

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