SOLUTION: Write the equation for the line: with y-intercept -1 and perpendicular to 3x-2y=6. a. 3x+2y=6 b. 2x+3y=6 c. 2x-3y=-3 d. 2x-3y=3 e. 2x+3y=-3

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Question 526373: Write the equation for the line: with y-intercept -1 and perpendicular to 3x-2y=6.
a. 3x+2y=6
b. 2x+3y=6
c. 2x-3y=-3
d. 2x-3y=3
e. 2x+3y=-3
Answer by oberobic(2304) (Show Source):
You can put this solution on YOUR website!
Write the equation for the line: with y-intercept -1 and perpendicular to 3x-2y=6.
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y = mx + b
y = mx -1 will have a y-intercept of (0,-1)
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Get 3x -2y = 6 into slope-intercept form.
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3x -2y = 6
-2y = -3x +6
y = 3/2*x +3
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The line perpendicular to this line will have a slope that is the inverse reciprocal of m = 3/2
which is -2/3 and b = -1.
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y = -2/3*x -1
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y-intercept = (0,-1)
x-intercept = the point where y = 0. So set y=0 and solve for x.
0 = -2/3*x -1
2/3*x = -1
2x = -3
x = -3/2
(-3/2, 0)
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In the following graph:
the red line is y = 3/2*x +3
the green line is y = -2/3*x -1
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Looking back at the question, it asks for the equation in standard form.
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y = -2/3*x -1
multiply by 3 to eliminate fraction
3y = -2x -3
add 2x to both sides
2x +3y = -3
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Done.