# 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.

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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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: $$y=-9x+26$$