Question deals with xy plane and graphing of equation/function?
143489
A line is typically defined as y=mx+b where the line has a slope of m. \n\nIf b were 0, the line would run through the origin and quadrants 1 and 3. To get a perpendicular line, you need a line that runs through quadrants 2 and 4.\n\nTo find this line, one simply inverts the coefficient of the slope, m, and reverses the sign of m.\n\nIn this case, you need to solve the original equation for y.\n\n1. 3x-4y=0 (original)\n2. 4y=3x\n3. y=3/4x\n\nFor the original line, the slope is 3/4. The slope of a perpendicular line is the negative inverse, or -4/3.\n\nSo, a perpendicular line is y=-4/3x + c where c can be any number--and in the answer choices, it's 12.
958831
Draw the graph of y = x^3\nThe (x-1) part shifts the graph to the right by 1.\nThe +4 part shifts the graph up by 4.\n(0,0) lies on y = x^3\n(1,4) lies on y = (x-1)^3 + 4\nNote that the x-coordinate increased by 1 and the y-coordinate increased by 4.
635075
Graph X=-4 with dotted lines\n\nthen color everything below the line.
1124994
you can use the y=mx+b formula for a line.  \n\ny is the y-coordinate of a point\n\nm is the slope, x is the x-coordinate of a point\n\nb is the y-intercept (where the line touches or intercepts the y-axes).  \n\nsince you know the y intercept of the line (passes through origin, so it's 0), the value of b would be 0 and  you also know the slope of the line, which is two, the equation for the line would look like this.\n\ny=2x + 0 or y=2x\n\na point on the line would have coordinates that would fit the equation ---- y has to be two times x; x has to be 1/2 of y.\n\nhere are some points on this line: (0,0), (1,2), (-1,-2), (2,4), (-2,-4).\n\nhope that helped :)
803558
1.\nc=(xy^2-1)/y\ndifrentiate w.r.t x\n(y(y^2 + 2xyp)-p(xy^2-1))/y^2=0\ny^3 + 2xy^2p - pxy^2 + p=0\ny^3 +xy^2p +p=0\nwhere p=(dy/dx)\n2.\nsimilarly diffrentiate \n(x+y^2)/x^2=-c\nto get\n2(x^2)yp - x^2 - 2xy^2=0\nthanks
707539
x = (y^2 + 2y -1) / 2\ndx=ydy+dy\n1=(y + 1 )dy/dx\ndy/dx=1/(y+1)\nd2y/dx2 = -1 / (y+1)^2
117178
Well, your third question is incomplete..\n\nBut I can answer the first two:\n\nIf you have an equation, assuming we're on cartesian coordinates, the simplest thing to do is to solve the Y variable to a couple or more X variables.\nLike:\nY=3x + 1\n\nx=0, Y= 3(0) + 1 = 0 + 1 = 1    (0,1)\nx=5, Y= 3(5) + 1 = 15 + 1 = 16  (5,16)\nand so on...\n\nThen you plot the coordinates on the graph and unite the resulting dots with a curve. In my example it should yeild a straight line.\n\nGraphs help describe trends on phenomenons that are tied to the equations.
318213
eh? you using simultaneous equations with a straight line equation?\n\ny = mx + c is a straight line equation, where m is the gradient & c is where the line cuts the y axis.\n\nThere for lets say y = -2x + 8:\ny = mx + c\nCuts x-axis Put y = 0\n-2x + 8 = 0\n-2x = -8\nx = -8/-2\nx = 4\n\nHope that was correct :| lol
133824
do your own homework!\n\nx=4, y=2, z=3
582742
Graph the line 3x + 4y = 12. \nIt divides the plane into one section where 3x + 4y < 12 and one where 3x + 4y > 12\n\nCheck to see see which side of the line (0,0) is on. It satisfies the inequality,  so shade the half plane that contains (0, 0) it's in the solution set.\n\nGraph the line x + 3y = 6. Again, check (0, 0) it satisfies that inequality, so shade everything on that side of the second line.\nNow draw the lines x = 0 and y = 0 (y axis and x axis)\nThose are the boundrys of your solution.
812734
The easiest way to graph this equation is to plug in 0 for x and get one point, then plug in 0 for y and get another, then draw the line that connects the two points.\n4(0) - 3y = 24\n-3y = 24\ny = -8\n(0, -8)\n\n4x -3(0) = 24\n4x = 24\nx = 6\n(6, 0)
379867
This is a typical function composition homework problem.\n\nExample:\nSuppose we have two functions of a variable x, \n\nf(x) = 1/x \n\nand\n \ng(x) = 1/x, \n\nthen \n\nf(g(x))\n= f(f(x)) \n= 1/(f(x)) \n= 1/(1/x)\n= x\n\nIt is given in this example that f(x) = g(x) = 1/x. Therefore, f(f(x)) = x. \n\nNow, f(f(x)) = f(x) \n\ncan be written \n\nx = 1/x.\n\nModifying this equation by cross multiplying give us x^2 = 1. Solving this equation by a method of your choice (factoring, quadratic formula, completing the square, square root property, etc.) gives x = 1 or x = -1.\n\nLet's check each of these answer. \nx = -1:\nf(-1) = 1/(-1) = -1 = x\n\nx = 1:\nf(1) = 1/(1) = 1 = x\n\nSo, there you have it: x = -1, 1.\n\nIf you have a graphing calculator, then graph y = x and  y = 1/x. Notice where the two graphs touch. That's right, at -1 and 1. \n\nDONE!
913484
are you talking about a polynomial :\na + bx +cx^2 + dx^3 +...\n\nbecause those a,b,c,d... do not appear any where on the graph... you have to look at the intercepts and the extreama, and the inflection points to get any good idea about the shape of the graph
946761
well to solve the first equation (its a line plot)\n3y+1[-1]=2x+16[-1]\n3y=2x+15\nif x=0, y=5 (y intercept)\nif y=0, x=-7.5 (x intercept)\n\nthe second line graph\n3y+5[+4]=2x\n3y+9=2x\nif x=0, y=-3\nif y=0, x=4.5\n\nNow, these lines are not equal, but do you have to plot both lines to prove? Your question is not clear.
549653
Subtract 2x from each side\n-y = 0 - 2x\nMultiply each side by -1\ny = 2x
763572
Hi!\n\nSo, what you are looking at is a linear equation.  You can tell this because there is only one instance of the variable x, and it is not raised to any power.  So, the graph will take the form of a line.\n\nAll linear equations take the form f(x) = mx + b\n\nWhere m is typically called the "slope" and b is called the "y-intercept".   The y-intercept is the point on the graph where the function intercepts the y-axis (the one that goes from top to bottom on the graph).  So, right away you can tell that the y-intercept in your equation is -5 (negative 5).  What this means is that the graph intercepts the y-axis at the -5, or in other words, there is a point on the graph at the location (0,-5).  You can put a dot there.\n\nThe next thing you need to see is the slope.  In you equation, the slope is -2 (negative 2).   Slope really means "rise over the run", or in other words, how much the graph rises for every point it goes to the right.  A slope of negative 2 means that for every increase in x of one unit, the y value decreases by negative 2.   \n\nSo, starting at the point (0,-5) which we determined above, go down 2 units and to the right one unit (putting you at the point (1,-7).  That's another point.  You can do it again and find the next point which is (2,-9) and put another point.  You now can put your ruler on the graph and draw the rest of it.\n\nIt's good to understand how this type of equation works.  You could have also made a table of x values and y values, and simply computed a series of y values for a series of x values (that you picked).  Then you could have drawn the graph also.  But understanding this type of equation will help you in the future.
879256
Zeroes: -3\ny-int: 2\nVA: x=1/2\nHA: y=-1/3\nThe graph looks like this: one wing opens on the right down and the other opens on the right up.