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nicole
11-05-2013, 06:17 AM
Which of the following is the equation of the line that is perpendicular to line 2x+3y=9 and passes through the point (1,2)?

(A) y=-\frac{2}{3}x+\frac{1}{2}

(B) y=-\frac{3}{2}x+\frac{1}{2}

(C) y=\frac{3}{2}x+\frac{3}{2}

(D) y=\frac{3}{2}x+\frac{1}{2}

(E) y=-\frac{3}{2}x-\frac{1}{2}

Thanks!;);)

Brynlee
11-05-2013, 06:18 AM
First we must find the slope of the line 2x+3y=9 . Thus, we must rewrite the equation to slope-intercept form i.e. y=ax+b where a is the slope.

So, the equation can be written as 2x+3y=9 \Rightarrow y=-\frac{2}{3}x+3.

The slope of a line which is perpendicular to the previous line is equal to \frac{3}{2} .

Thus, the required equation will be in the form of
y=\frac{3}{2}x+b

Due to the fact the this line passes through the point (1,2), we have to plug in the coordinates of this point to the equation and obtaining with this way the value of b,
2=\frac{3}{2}1+b \Rightarrow b=2-\frac{3}{2}=\frac{1}{2}

Finally the equation will be given by the formula
y=\frac{3}{2}x+\frac{1}{2}

Therefore the correct answer is (D).

nicole
11-05-2013, 06:18 AM
Thanks Brynlee!!