SOLUTION: Two perpendicular lines intersect on the x-axis. The equation of one line is 3x-5y+6=0. What is the equation of the other line?
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Question 203012: Two perpendicular lines intersect on the x-axis. The equation of one line is 3x-5y+6=0. What is the equation of the other line? Answer by solver91311(24713) (Show Source):
Solve the given equation for , that is put it into form. Then determine the slope of the given line by inspection of the coefficient on .
Knowing the slope of the given line will tell you the slope of the perpendicular line, because:
Since the two lines intersect on the -axis, you can find the point of intersection by determining the -intercept of the given equation. Substitute 0 for in the original equation and then do the arithmetic to solve for . The -intercept is a point of the form where is the value you just calculated.
With the slope of the desired line and the -intercept point use the point-slope form to derived the desired equation:
where is the given point and is the slope determined above.
