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Lilmike234
 one year ago
What is the equation, in standard form, of the line passing through the points (2,3) and (4,2) ?
Lilmike234
 one year ago
What is the equation, in standard form, of the line passing through the points (2,3) and (4,2) ?

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mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1First, find the slope of the line. You can use the two given points for that.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1The slope of the line that passes through points \((x_1, y_1)\) and \((x_2, y_2) \) is \(slope = m = \dfrac{y_2  y_1}{x_2  x_1} \)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1To find the slope, subtract the ycoordinates, and divide by the difference of the xcoordinates. Make sure you subtract the ycoordinates and the xcoordinates in the same order. Can you try this and tel me what you get?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Correct. dw:1437619975077:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Notice what I did above. I did it both ways. Using one point first one time and the other point first the other time to do the subtractions. It does not matter which point you choose as the first point. The important thing is to not mix the order when you subtract. As you can see both ways give the same answer, and you got it right.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Now that we have the slope, we do the next step.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1The equation of a line given two points is: \(y  y_1 = \dfrac{y_2  y_1}{x_2  x_1} (x  x_1)\) or simply \(y  y_1 = m (x  x_1)\) when you let m = the slope. y and x above are the y and x of the equation. \(x_1\) and \(y_1\) are the x and ycoordinates, respectively, of a point on the line.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1We already have the slope, so we can use the form \(y  y_1 = m(x  x_1)\) Since we know the \(slope = m = \dfrac{1}{2} \), we replace m with the slope \(y  y_1 = \dfrac{1}{2} (x  x_1) \)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1All that is left to do is to replace \(x_1\) and \(y_1\) with the coordinates of one of the points. You can use whichever point you want of the two given points.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Let's use point (2, 3). We replace \(x_1\) with 2 and \(y_1\) with 3. \(y  3 = \dfrac{1}{2}(x  2)\)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1You already have the equation of the line. Now you can put the equation in standard form or slopeintercept form if you'd like to.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1\(y  3 = \dfrac{1}{2}(x  2)\) \(2y  6 = (x  2) \) \(2y  6 = x + 2\) \(2y = x + 8\) \(y = \dfrac{1}{2} x + 4\)

lilmike234
 one year ago
Best ResponseYou've already chosen the best response.1The answer choices are 1. y=5/2x+8 2. 5x+2y=16 3. 2x3y=9 4. 5x2y=16

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Are you sure those are the choices of the same problem?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1We have a slope of 1/2 None of those choices have a slope of 1/2

lilmike234
 one year ago
Best ResponseYou've already chosen the best response.1Well those were the answer choices

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Let's look at your choices and put every equation in the slope intercept form, y = mx + b. 1. y=5/2x+8 slope = 5/8 2. 5x+2y=16 2y = 5x + 16 y = 5/2 x + 8 slope 5/8 3. 2x3y=9 3y = 2x + 9 y = 2/3 x  3 slope 2/3 4. 5x2y=16 2y = 5x + 16 y = 5/2x  8 slope 5/2 As you can see, none of your choices have slope 1/2 None of them are answer to this question. Are you sure these are the given answers to this question and are you sure you copied the points correctly when you posted the question?
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