Question

Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form. Passing through (3,-1) and perpendicular to the line whose equation is x-9y-5=0 Write an equation for the line in point-slope form and slope-intercept form.

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asked 2021-06-02
Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form.
Passing through (3,-1) and perpendicular to the line whose equation is x-9y-5=0
Write an equation for the line in point-slope form and slope-intercept form.

Answers (1)

2021-06-03

Step 1
We find the slope of \(x-9y-5=0\) by writing it in \(y=mx+b\) form
\(x-9y-5=0\)
\(9y=x-5\)
\(y=\frac{x-5}{9}\)
\(y=\frac{1}{9}x-\frac{5}{9}\)
\(m=\frac{1}{9}\)
So, slope of the perpendicular \(=-9\)
Step 2
Given that the line is passing through (3,-1)
And we got slope \(=-9\)
So point slope form is:
\(y-(-1)=-9(x-3)\)
\(y+1=-9(x-3)\)
Step 3
Using the point slope form we find the slope intercept form
\(y-(-1)=-9(x-3)\)
\(y+1=-9(x-3)\)
\(y+1=-9x+27\)
\(y=-9x+26\)
Answer: Point slope: \(y+1=-9(x-3)\)
Slope intercept: \(y=-9x+26\)

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