find the equation of the line that passes through (2, -7) and is parallel to 5x + 4y = 7.
2007-01-31 14:22:28 · 13 answers · asked by judykharrison 1 in Science & Mathematics ➔ Mathematics
isolate y and find m:
y= (-5/4)x+7/4
m=-5/4
so that line has same m
and then
y=(-5/4)x+b
-7=(-5/4)(2)+b
find b, and you are done.
2007-01-31 14:26:41 · answer #1 · answered by Anonymous · 0⤊ 0⤋
If 5x + 4y = 7 then y = (-5/4)x + 7/4. This is the equation of a line with slope -5/4. Any line parallel to it has the same slope. If a parallel line contains the point (2,-7) then the point-slope form of its equation is y - (-7) = (-5/4)(x - 2), so 4(y + 7) = -5( x - 2).
Then 4y + 28 = -5x + 10, or 5x + 4y = -18 is the equation of the line that you want.
2007-01-31 14:34:42 · answer #2 · answered by wild_turkey_willie 5 · 0⤊ 0⤋
This is actually very simple if you stop and think for a moment. The equation of the line is parallel to 5x + 4y = 7, which means that it will have the same slope... in other words, the same x to y ratio.
This means that the equation you seek is going to have the same 5x + 4y in it; the only thing that will change is the constant (7).
To find what your new constant is, you simply need to satisfy the equation of the line (figure out what number on the right will make the line pass through (2, -7)). To do this, simply substitute in the x and y coordinates that you are given (2, -7) into 5x + 4y.
You'll get 5(2) + 4(-7) which equals -18
This means your new equation will be 5x + 4y = -18.
2007-01-31 14:29:17 · answer #3 · answered by Anonymous · 0⤊ 0⤋
Parallel lines have the same slope. In ax + by = c, the slope is -a/b.
So for 5x + 4y = 7, the slope is -5/4, and all lines parallel have the form 5x + 4y = c. To find the line through (2, -7), plug the coordinates of the point into the equation, getting 5x + 4y = c = 5(2) + 4(-7) = -18.
So 5x + 4y = -18
2007-01-31 14:27:37 · answer #4 · answered by Philo 7 · 0⤊ 0⤋
The answer is 4y = - 5x - 18
In order to have parallel lines, the slope has to be the same for both equations.
Y = mX + b is the slope intercept form for this formula.
Putting the original formula in slope intercept form would be
y = - 5/4 X + 7/4.
Since you know the slope will be the same for parallel lines, you can insert the given coordinates (2,-7) into this formula. 2 represents x and -7 represents y so you get
-7 = -5/4(2) + b.
Solving for b you will get
b = - 9/2.
To get your new formula, put the x and y back into the equation and write it as the first given equation was written and you get the answer I gave you.
2007-01-31 14:48:06 · answer #5 · answered by eiplanner 3 · 0⤊ 0⤋
If one has to be parallel to the other, then they need the same slope. put the second equation in slope intercept form y= mx +b which gives you y=(-5/4)x + (7/4) The -5/4 is your slope. Now start your second NEW equation with that slope y = (-5/4)x + b. The only thing left to do is find b, which is what makes the line pass thru (2, -7). Plug in the x and y from the point into your new equation -7=(-5/4)*2 + b. Then solve for b. b= -4.5 So your final new equation is y= (-5/4)x - 4.5 :)
2007-01-31 14:30:42 · answer #6 · answered by munkeyman111 1 · 0⤊ 0⤋
First get y by itself so you can get the slope:
5x + 4y = 7
4y = -5x + 7
y = -5/4 x + 7/4
Slope is -5/4, the number in front of x, which will also be the slope of any parallel line.
If you use the point slope form of a line, you already have enough to get the answer. Otherwise, start with y = -5/4x + b, plug in 2 for x and -7 for y to find what b is.
2007-01-31 14:28:49 · answer #7 · answered by hayharbr 7 · 0⤊ 0⤋
5 times x + 4 times y =7
2007-01-31 14:29:51 · answer #8 · answered by ♥less 5 · 0⤊ 0⤋
5x+4y =7
rewrite it to make y the subject of formula.i.e y=7/4 - 5x/4
the gradient(m) = -5/4
y= mx + c
y=-7 & x= 2
-7 =(-5/4)2 +c
-7 = -5/2 + c
c = -9/2
the equation of the line that passes through (2, -7) and is parallel to 5x +4y = 7 is y = -5/4x -9/2
2007-01-31 15:09:06 · answer #9 · answered by la boucle 1 · 0⤊ 0⤋
you want y = mx + b format.
5x + 4y = 7
4y = -5x + 7
y = -(5/4)x + (7/4)
-(5/4) is the slope. A parallel line will have the same slope.
then substitute for x, m, and y.
y = mx + b
-7 = -(5/4) (2) + b
-7 = -10/4 + b
b = -4.5
so your parallel line is
y = -(5/4)x - 4.5
2007-01-31 14:30:56 · answer #10 · answered by Matthew 2 · 0⤊ 0⤋
where's the tricky part?
you want to find the equation of line
you are given one point that it passes through
(to find the equation, you will either need to find another point the line passes through, or the slope of the line)
you are given the equation of another line that is parallel to the line you want to find. if it is parallel to it, then it has the same slope.
wow that was pretty easy. where is the trick?
2007-01-31 14:27:55 · answer #11 · answered by Anonymous · 0⤊ 0⤋