SOLUTION: Find the equation of the line which is parallel to the line 2y + x=3 and passes through the midpoint of (-2,3)and (5,4)

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Question 1187696: Find the equation of the line which is parallel to the line 2y + x=3 and passes through the midpoint of (-2,3)and (5,4)
Found 3 solutions by josgarithmetic, MathLover1, MathTherapy:
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
Slope of the given and the required line is -1%2F2.
Midpoint of the two given points is (3/2, 7/2).
How those, is omitted here.

If you continue with point-slope form, then y-7%2F2=-%281%2F2%29%28x-3%2F2%29, and you do what you need from here.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


an equation of the line is:
y=mx%2Bb where m is a slope and b is y-intercept
if the line is parallel to the line 2y+%2B+x=3, means the line will have same slope
find a slope of
2y+%2B+x=3......solve for y
y+=-x%2F2%2B3%2F2=> slope m=-1%2F2
so far, equation is
y=-%281%2F2%29x%2Bb
if the line passes through the midpoint of (-2,3)and (5,4), we need to find midpoint M
M= (%28-2%2B5%29%2F2,%283%2B4%29%2F2)= (3%2F2,7%2F2)
use midpoint to calculate b
7%2F2=-%281%2F2%29%283%2F2%29%2Bb
7%2F2=-%283%2F4%29%2Bb
7%2F2%2B3%2F4=b
b=17%2F4
and your line is
y=-%281%2F2%29x%2B17%2F4







Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

Find the equation of the line which is parallel to the line 2y + x=3 and passes through the midpoint of (-2,3)and (5,4)
Midpoint of (- 2, 3) and (5, 4): 

Equation that's parallel to 2y + x = 3, or x + 2y = 3, and passing through point matrix%281%2C5%2C+%22%28%22%2C+3%2F2%2C+%22%2C%22%2C+7%2F2%2C+%22%29%22%29: