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Question 4037: A line has a y-intercept of (0,2) and is perpendicular to the line with equation 2x-3y=6. Write the equation of the line.
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Your answer can be written in the slope-intercept form of the equation for a line: y = mx + b
So you need to find the slope, m, and the y-intercept, b.
The y-intercept is given as 2.
You can get the slope from the given line to which your new line is perpendicular.
Perpendicular lines have slopes that are the negative reciprocal of each other.
The slope of the given line can be found by re-writing the equation (2x-3y=6)in the slope-intercept form: y = mx + b
2x - 3y = 6 Add 3y to both sides.
2x = 3y + 6 Subtract 6 from both sides.
2x - 6 = 3y Divide both sides by 3.
(2/3)x - 2 = y or y = (2/3)x - 2 Compare with: y = mx + b: m = 2/3
The negative reciprocal of 2/3 is -3/2
The equation of the new line is: y = -(3/2)x + 2
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