SOLUTION: how do you find for y if you have this problem (3,-7) 2x-5y=3

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Question 1131741: how do you find for y if you have this problem
(3,-7) 2x-5y=3

Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Makes no sense.


Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
given:
point (3,-7)
equation of a line: 2x-5y=3
case 1:
since you have nothing else, I guess you need to prove does this point lie on givren line
2x-5y=3...........plug in x and y coordinates of the given point
2%2A3-5%28-7%29=3
6%2B35=3
39%3C%3E3=> point (3,-7) does not lie on given line

case 2:
you might have to find equation o another line that is parallel or perpendicular to given line and passes through given point
so, if you need to find a line y=mx%2Bb that is parallel to given line and passes through given point, you need
first write your line in slope-intercept form (solve it for y):

2x-5y=3
2x-3=5y
y=%282%2F5%29x-3%2F5=>slope is 2%2F5
since parallel lines have same slope, so far your equation is
y=%282%2F5%29x%2Bb.........use point (3,-7) to ind b
-7=%282%2F5%293%2Bb
-7=%286%2F5%29%2Bb
-7-%286%2F5%29=b
b=-35%2F5-6%2F5
b=-41%2F5

and, parallel line is: y=%282%2F5%29x-41%2F5



case 3:
if you need to find a line y=mx%2Bb that is perpendicular to given line and passes through given point,
perpendicular line will have a slope negative reciprocal of the %282%2F5%29 and it is:
-1%2F%282%2F5%29=-5%2F2

y=-%285%2F2%29x%2Bb.........use point (3,-7) to ind b
-7=-%285%2F2%293%2Bb
-7=-%2815%2F2%29%2Bb
-7%2B%2815%2F2%29=b
-14%2F2%2B15%2F2=b
b=1%2F2
and, perpendicular line is: y=-%285%2F2%29x%2B1%2F2