Determine the slope of the line that passes through (2, 2) and (5, 8).?
92968
The slope is 2. (Rise / Run)\n\n(8-2) / (5 - 2) = 6 / 3 = 2
910261
Slope = m\n= y2-y1&#92;x2-x1 \n= -4-6/-3-2\n = -10&#92;-5\n=2\n\nnote: / means divided by\n\nthe slope of y= 2&#92;3x-4 is 2&#92;3
771497
No - the slope is going to be a number, not an equation.\n\nd/dx (2x^2) = 4x\n\nAt x = -2, the slope will be -8.\n\nThe equation of the tangent LINE would be\n\ny + 8 = -8(x + 2)\n\ny = -8x - 24, as you have it.\n\nAnd no - getting the terminology right is not a minor point.
813141
both are easy\n\nbecause slope is -5 so\n\neqution of line is\n\ny = -5x+c\nput y = 6 and x = 3 to get\n\n6= -15+c \nor c= 21\n\nequaton of line \n\ny = - 5x + 21\nor 5x+y - 21 = 0 as you got it\n\nNow for the area\n\nit cuts y axis at x =0\nso y = 21\n\nwhen it cuts x axis at y =0 or x = 4.2\n\nit is a right triangle\nso area = 21 *4.2/2 = 21*2.1 = 44.1
134706
I'd plot the points and figure out the slope (vertical change/horizontal change).  In this case, it would be -1 [2 / -2].  Then trace out the line to see at what point it crosses the Y axis.  In this case, it would be -2.  Then plus those numbers in the the equation "Y = (slope)X + (intersection of Y axis)"  So, if I'm not mistaken, the solution should be "Y = -X - 2".
407712
slope = -0.25\nintercept = 1
1101719
Step 1: Find the slope of the line x-2y = 2.  Call it m. \n\nStep 2: Find the derivative f'(x) of the function f(x) = (x-1)/(x+1).\n\nStep 3: Find all values of x where f'(x) = m.\n\nStep 4: For each such value, find its corresponding y-coordinate by setting y=f(x), and then find the equation of the line that goes through that point with slope m.\n\nGood luck!
743965
If you can find the slope, you use the formula\n\ny - y1 = m(x-x1) where y and x are in general and y1 and x1 are the x and y values from ONE point. Pick either, it doesn't matter. So...\n\nThe slope is -2.\n\ny - 8 = -2 (x - - 2)\n\ny-8 = -2x - 4\n\ny = -2x + 4
754086
the slope will be (0 + 9) / (-8 +7) = 9/-1 = -9 --> m = -9\n\nnow take a point and plug it in to the formula y = mx + b.\n0 = -9(-8) + b ---> b = -72\n\nnow your done. y = -9x - 72
32903
if you are given points (ex. (2,1) and (3,5) you can use this formula:\nm (slope) = y2-y1 / x2-x1\nso: 5 - 1 / 3-2 = 4/-1 or -4\n\nif you are given the equation of a line you can use this:\nx - ay = b\ny = -x + b / -a\nex.x-3y = 15\n-3y = -x + 15\ny = x/3 + 15\nso the slope is:\nx/3 = 1/3\nm(slope) = 1/3\nalways look for the coefficient of x and that is the slope.\n\nyou can also use this when you are given an angle:\nm (slope) = tan alpha
819556
Hey, here's the setup for these types of problems.\nYou want the equation in the form of y = mx + b\nsince we know that x = 2, y = -7, and m = -1/5, we can plug these values into that equation to find the equation of the line that passes through the desired point. SO:\n-7 = (-1/5)(2) + b\n-7 = (-2/5) + b\nb = (-7)+(2/5)\nb = -33/5\nso the equation for the line is:\ny = (-1/5)x - (33/5)\n\nhope that helps!!
1121252
slope = m\nperpendicular slope = (-1)/m\n\nslope = (y2-y1)/(x2-x1)\nslope = (2-5)/(4-2)\nslope = -3/2\n\nperpendicular slope = 2/3
253663
Slope is the "change in y" divided by the "change in x" (AKA "rise" over "run").\n\n(x1, y1) = (-2, 4)\n(x2, y2) = (2, -1)\n\nThus:\n\nm (slope) = "delta y"/"delta x" = rise/run\nm = (y2 - y1)/(x2 - x1)\nm = (-1 - 4)/(2 - (-2))\nm = -5/4\n\nrun = 4, rise = -5
226683
The equation of the tangent at any point is f'(x)=3*(x^2).\n\nAt x=2, f'(2)=12, f(2)=8.\n\nSo the line has slope 12 and passes through the point (2,8).\n\ny - 8 = 12 * (x - 2) is the equation of the tangent line.
943301
Use the standard equation for a line going through two points.\n\nI.e. for two points (x1,y1), (x2,y2) the equation is : \n   (y2-y1)/(x2-x1) = (y-y1)/(x-x1).\n\nIn this case we have (x1,y1)=(0,-5) and (x2,y2)=(8,9), so\n   (9-(-5))/(8-0) = (y-(-5))/(x-0)\nwhich computes to\n   14/8 = (y+5)/x\nor, in standard format\n   y = (7/4)*x - 5\n\nIf you now check (fill in those two points) you will see it is the correct equation for both.\n\nHope this helps :-)
877049
use the slope formula.\n\ny sub 2 minus y sub 1 divided by x sub 2 minus y sub 1\n\nthen you get 1-5 divided by 0-2\n\nthen you get -4 divided by -2\n\nthe answer is 2
941794
first you find the slope using formulae: \nm = (y2-y1)/(x2-x1)\nm = (-1-7)/(5+3)\nm = -8/8\nm = -1\n\nthen you substitute this into the formulae:\ny = mx + b\ny = -x + b (use one of the coordinates to find b)\n7 = -(-3) + b\n7 = 3 + b\n7 - 3 = b\nb = 4 (substitute back into the equation)\n\ny = -x + 4 (there goes your answer!)