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Question 811474: Find the equation of the line that passes through the point (-6, 7) and is parallel to the line 5x-3y=5. Write your answer in standard form and slope intercept form.
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! 5x - 3y = 5
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into standard form:
5x + (-3)y = 5
A B C = 5 -3 5
plug A B C into: https://sooeet.com/math/linear-equation-solver.php
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slope (m) = 1.66666667 = 1+2/3 = 5/3
y-intercept = -1.66666667 = -5/3
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parallel lines have equal slopes:
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if the new line passes through (-6, 7)
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new line into point-slope form:
x1 y1 m = -6 7 1.66666667
plug x1 y1 m into: https://sooeet.com/math/linear-equation-solver.php
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slope (m) = 1.66666667 = 1+2/3 = 5/3 (as expected, new line has same slope as original line.)
y-intercept = 17
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result
y = (5/3)x + 17
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alternatively, put the original line in slope-intercept form:
5x - 3y = 5
3y = 5x - 5
y = (5/3)x - (5/3)
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again we see:
slope (m) = 5/3
y-intercept = -5/3
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since the new line passes through (-6, 7), put the new line in point-slope form:
y - y1 = m(x - x1)
y - 7 = (5/3)(x + 6)
y - 7 = (5/3)x + 10
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same result:
y = (5/3)x + 17
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