SOLUTION: HI please help me with this question Find an equation of the line that is perpendicular to 2x-3y+6=0 and has the same x intercept as 3x+7y+9=0. thanks for any help coming th

Question 118055: HI
please help me with this question
Find an equation of the line that is perpendicular to 2x-3y+6=0 and has the same x intercept as 3x+7y+9=0.
thanks for any help coming this way.
Answer by ilana(307) (Show Source): You can put this solution on YOUR website!
Perpendicular lines have opposite reciprocal slopes. So we need to find out the slopes of our lines. If 2x-3y+6=0, then 3y=2x+6 and y=(2/3)x+2, so the slope is 2/3. So the perpendicular line has a slope of -3/2. Now we need the x-intercept. The x-intercept is the point with a y-coordinate of 0. So going back to the equation y=(2/3)x+2, plugging in a 0 for y gives 0=(2/3)x+2. So (2/3)x=-2 and x=-3. So both this line and the perpendicular line have contain the point (-3,0). So the equation with the point (-3,0) and a slope of -3/2 is the answer. Using the point-slope form of a line, y-0=(-3/2)(x+3), or y=(-3/2)x-(9/2). (Or even 3x+2y+9=0)
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