Solve
Step
3x + 5y = -6
5y = -3x – 6
y = (-3/5)x – 6/5
m = -3/5
(Section 2.2)
So the new m = 5/3
y – 3 = 5/3(x – (-1))
y - y1 = m(x – x1)
3(y – 3) = 3[5/3(x + 1)]
3y – 9 = 5(x + 1)
3y – 9 = 5x + 5
-5x + 3y = 14
Find the equation of the line that contains the point (-1,3) and is perpendicular to the line 3x + 5y = -6
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Solve |
Step |
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3x + 5y = -6 |
First find the slope of by solving for y |
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5y = -3x – 6 |
Subtract 3x from both sides |
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y = (-3/5)x – 6/5 |
Divide both sides by 5 |
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m = -3/5 |
The
new slope will be the negative reciprocal of -3/5. (Section 2.2) |
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So the new m = 5/3 |
Note:
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y – 3 = 5/3(x – (-1)) |
Now use point slope form y - y1 = m(x – x1) |
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3(y – 3) = 3[5/3(x + 1)] |
Multiply by 3 |
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The fraction is gone now. |
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3y – 9 = 5(x + 1) |
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3y – 9 = 5x + 5 |
Get x and y on the same side |
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-5x + 3y = 14 |
Done Þ General Form |
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Check |
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You can check one point |
and the slope. |
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(-1,3) |
-5x + 3y = 14 |
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-5x + 3y = 14 |
3y = 5x + 14 |
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-5(-1) + 3(3) =14 |
y = (5/3)x + 14/3 |
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5 + 9 = 14 |
m = 5/3  |
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14 = 14 |
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