Math

QuestionFind the equation of line vv that is perpendicular to y=94x+1y=-\frac{9}{4} x+1 and passes through the point (3,2)(-3,2).

Studdy Solution

STEP 1

Assumptions1. Line uu has the equation y=94x+1y=-\frac{9}{4} x+1 . Line vv is perpendicular to line uu
3. Line vv passes through the point (3,)(-3,)4. The slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line

STEP 2

First, we need to find the slope of line uu. The slope of a line in the form y=mx+by=mx+b is mm.
So, the slope of line uu is 94-\frac{9}{4}.

STEP 3

Next, we need to find the slope of line vv, which is perpendicular to line uu. The slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line.
So, the slope of line vv is the negative reciprocal of the slope of line uu.
mv=1mum_v = -\frac{1}{m_u}

STEP 4

Plug in the value for the slope of line uu to calculate the slope of line vv.
mv=194m_v = -\frac{1}{-\frac{9}{4}}

STEP 5

Calculate the slope of line vv.
mv=194=49m_v = -\frac{1}{-\frac{9}{4}} = \frac{4}{9}

STEP 6

Now that we have the slope of line vv, we can use the point-slope form of a line to find the equation of line vv. The point-slope form of a line is yy1=m(xx1)y-y1=m(x-x1), where (x1,y1)(x1,y1) is a point on the line and mm is the slope of the line.

STEP 7

Plug in the values for the slope and the point (3,2)(-3,2) to find the equation of line vv.
y2=49(x+3)y-2=\frac{4}{9}(x+3)

STEP 8

Finally, we can simplify this equation to put it in the form y=mx+by=mx+b.
y=4x+26y=\frac{4}{}x+\frac{26}{}So, the equation of line vv is y=4x+26y=\frac{4}{}x+\frac{26}{}.

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