#### • Class 11 Physics Demo

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#### • equation for standard form

Question:Can someone please explain it to me? And the problem is y=3/5x+7/5 with choices of 3x-5y=7, 5y=3x+7, 3x-5y=-7, and -3x = -5y+7. Is there anyway to figure it out with a graphing calculator?

Answers:Sure. My graphing calculator is a pencil. The usual "standard form" for the equation of a line looks like ax + by = c, where a,b,c are constants. If any of the numbers are fractions, it's usual to multiply by the least common multiple of the denominators to get all integers. First write the equation as: (3/5)x + 7/5 = y .... with x on the left side, then (3/5)x - y + 7/5 = 0 .... subtract y from both sides (3/5)x - y = -7/5 .... subtract 7/5 from both sides 3x - 5y = -7 .... multiply both sides by 5 to clear the fractions That's one of your answers, but remember that: -3x + 5y = 7 .... after multiplying both sides by -1 is also in standard form, and some would prefer it because there is only one minus sign.

Question:Input in standard form the equation of the given line. The line that passes through (-2, 4) and is parallel to x - 2y = 6

Answers:first, try to think this problem through. take the line that you are given and write it in { y = mx + b } form, and just sit if off on the side for now, until later. x - 2y = 6 x - x - 2y = 6 - x -2y = -x + 6 -2y / -2 = -x/-2 + 6/-2 y = (1/2)x + -3 -----> slope is (1/2) , so the slope for the line you are trying to find must also be the same now, find the equation of the line through the point (-2, 4) using the formula: y - y1 = m(x - x1) ; where x1 and y1 is your point (x1, y1) and m is your slope, which we are using from the other equation by putting it in slope-intercept form. y - 4 = (1/2)(x - (-2)) y - 4 = (1/2)(x + 2) y - 4 = (1/2)x + (1/2)*2 y - 4 = (1/2)x + 1 y - 4 + 4 = (1/2)x + 1 + 4 y = (1/2)x + 5 ------> this is the equation of your line in "slope-intercept form or y=mx+b form" now, the form that you want it in is in standard form, which is: Ax + By = C, where A, B, and C are all constants. Note: we don't really have to worry about the constants, because all we are doing now, is basically just rearranging the equation that we just found above { y = (1/2)x + 5 } to be equal to C or 5 y = (1/2)x + 5 y - y - 5 = (1/2)x - y + 5 - 5 -5 = (1/2)x - y (1/2)x - y = -5 <------this is the equation of a line parallel to your other equation in standard form however, you can make it look nicer buy multiplying the whole equation by a constant of 2 2((1/2)x - y = -5) x - 2y = -10 <------simplified equation in standard form Note: (1/2)x - y = -5 <-----> = <------> x - 2y = -10 *****I hope that this helps some!!! Good Luck!!!*****

Question:Write an equation of a line in standard form for slope = undefined and passes through ( 1, 6) for some reason the answer sheets reads "x + 0y = 1" as the answer to the question; do u think the answer sheet is wrong?

Answers:the standard eqn of a line is y = mx + c where, y = y coordinate x = x coordinate c = constant m = slope =y / x m = undefined eqn of line becomes 6 = -m + c

Question:How would you write the standard form of an equation of the line that passes through the given point and has the given slope. please explain im really bad at math, (-2,7) m= -4 (-6,-7) m= -1 (10, 6) m=0 (5, -8) m=1/2 is this in standard form?

Answers:First lets find the y-intercept of each line using y = mx + b 1. (-2,7) m = -4 y = mx + b 7 = -4(-2) + b 7 = 8 + b -1 = b Now lets put slope(m) and y-intercept (b) in the equation y = -4x - 1 To put it in standard form, x and y have to be on the same side: 4x + y = -1 ....that is your answer for the first one. 2. (-6, -7) m = -1 y = mx + b -7 = -1(-6) + b -7 = 6 + b -13 = b y = mx + b y = -1x - 13 x + y = -13 is your equation for #2 3. (10, 6) m = 0 If your slope is zero, it is a horizontal line. A horizontal line has an equation of y = (a number). Since your y value in the point is 6, your equation will be: y = 6 4. (5, -8) m = 1/2 y = mx + b -8 = 1/2(5) + b Multiply through by 2 (common denominator) to get rid of fractions you get: -16 = 5 + 2b -21 = 2b -21/2 = b y = mx + b y = 1/2 x - 11/2 1/2x - y = 21/2 To write it without fractions, mutiply it through by 2 to get: x - 2y = 21 Hope this helps