Question #7356c

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Answer 1 · 2017-12-11T01:37:58

$-1/5x-6/5=y$

First, remember that the equation $-1/mx+b=y$ is perpendicular to $mx+b=y$

First, write $5x-y=3$ in the intercept form $y=mx+b$

$5x-y=3$
$5x=3+y$
$5x-3=y$

Since the slope is 5, the slope for the perpendicular line is $-1/5$

Since this line perpendicular to $5x-3=y$ passes through (4,-2), we can use the formula $m(x-x_1)=y-y_1$ to find the equation.

$-1/5(x-4)=y-(-2)$ We need to make this into the form $y=mx+b$

$-1/5(x-4)=y-(-2)$

$-x/5+4/5=y+2$
$-x/5+4/5-2=y$
$-x/5-6/5=y$
$-1/5x-6/5=y$
That is our answer! To prove this, simply graph these two points.

Desmos

Answer 2 · 2017-12-11T01:38:44

$y+2=-\frac{1}{5}(x-4)$

Perpendicular lines have slopes that are negative reciprocals of each other.

So the perpendicular line will have a slope of $-\frac{1}{5}$ .

Now we can write the equation in point-slope form:

$y-y_1=m(x-x_1)$

$\implies y+2=-\frac{1}{5}(x-4)$