Find the equation of the line parallel to 8 x - 16 y = 9 . and passing through the point ( 7 , -9 ).
How do i do this?? thank you
How do i do this?? thank you
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8x - 16y = 9
-16y = -8x + 9
y = (1/2)x - 9/16
Parallel lines have the same slopes:
y = (1/2)x + b
find b using the given point (7,-9):
-9 = (1/2)(7) + b
b = -25/2
Equation is:
y = (1/2)x - 25/2
- .--
-16y = -8x + 9
y = (1/2)x - 9/16
Parallel lines have the same slopes:
y = (1/2)x + b
find b using the given point (7,-9):
-9 = (1/2)(7) + b
b = -25/2
Equation is:
y = (1/2)x - 25/2
- .--
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Rewrite the equation in terms of y only:
8x - 16y = 9
16y = 8x - 9
y = 1/2*x - 9/16
This way it's easy to see what the slope of this line is (m=1/2), which is the same slope for the line you're trying to find. Parallel lines have identical slopes.
Now, given the point that this new line must cross, you plug them into the point-slope formula, which is:
y - y1 = m(x - x1),
where (x1,y1) is the point you are given.
Thus we have:
y - (-9) = (1/2) (x - 7)
y + 9 = 1/2*x - 7/2
y + 18/2 = 1/2*x - 7/2
y = 1/2*x - 25/2
8x - 16y = 9
16y = 8x - 9
y = 1/2*x - 9/16
This way it's easy to see what the slope of this line is (m=1/2), which is the same slope for the line you're trying to find. Parallel lines have identical slopes.
Now, given the point that this new line must cross, you plug them into the point-slope formula, which is:
y - y1 = m(x - x1),
where (x1,y1) is the point you are given.
Thus we have:
y - (-9) = (1/2) (x - 7)
y + 9 = 1/2*x - 7/2
y + 18/2 = 1/2*x - 7/2
y = 1/2*x - 25/2
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8 x - 16 y = 9
8 x - 16 y - 9 = 0
any line parallel to the above line is of the form
8 x - 16 y + c = 0------(1) [where c is a constant]
the above line passes through ( 7 , -9 )
8(7)-16(-9)+c=0
56+144+c=0
c=-200
substitute in (1)
8 x - 16 y - 200 = 0
x - 2 y - 25 = 0
2 y = x - 25
therefore y = (x/2) - (25/2)
is the required equation of the line ☺
8 x - 16 y - 9 = 0
any line parallel to the above line is of the form
8 x - 16 y + c = 0------(1) [where c is a constant]
the above line passes through ( 7 , -9 )
8(7)-16(-9)+c=0
56+144+c=0
c=-200
substitute in (1)
8 x - 16 y - 200 = 0
x - 2 y - 25 = 0
2 y = x - 25
therefore y = (x/2) - (25/2)
is the required equation of the line ☺
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You have to convert it out of standard form to slope intercept form, to find the slope and the y-intercept.
Since it has to be parallel, it has to have the same slope as 8x - 16y = 9.
So you subtract 8x from both sides, leaving -16y = -8x + 9. "y" can't be negative, so you have to change the signs of the whole equation, making it 16y = 8x - 9. Divide by 16 to get y, y = 1/2x - 9/16.
The slope is 1/2, so plug that into slope intercept form with the points (7, -9).
-9 = 1/2(7) + b.
-9 = 7/2 + b. b = -25/2.
So, the final equation is y = 1/2x - 25/2.
Sorry this probably didn't make much since. Email me if you need more help. purpleoutloud@yahoo.com
Since it has to be parallel, it has to have the same slope as 8x - 16y = 9.
So you subtract 8x from both sides, leaving -16y = -8x + 9. "y" can't be negative, so you have to change the signs of the whole equation, making it 16y = 8x - 9. Divide by 16 to get y, y = 1/2x - 9/16.
The slope is 1/2, so plug that into slope intercept form with the points (7, -9).
-9 = 1/2(7) + b.
-9 = 7/2 + b. b = -25/2.
So, the final equation is y = 1/2x - 25/2.
Sorry this probably didn't make much since. Email me if you need more help. purpleoutloud@yahoo.com
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The given line has slope 1/2, so the desired line has slope 1/2 and passes through (7, –9)
y = 1/2 x + b. Plug in the point to find b
–9 = 7/2 + b
b = –25/2
y = 1/2 x – 25/2
y = 1/2 x + b. Plug in the point to find b
–9 = 7/2 + b
b = –25/2
y = 1/2 x – 25/2
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8x-16y=9
-16y=-8x+9
y=1/2x-9/16
y+9=1/2(x-7)
y+9=1/2x-7/2
y=1/2x-25/2
-16y=-8x+9
y=1/2x-9/16
y+9=1/2(x-7)
y+9=1/2x-7/2
y=1/2x-25/2