Lilmike234
  • Lilmike234
What is the equation, in standard form, of the line passing through the points (2,3) and (4,2) ?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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mathstudent55
  • mathstudent55
First, find the slope of the line. You can use the two given points for that.
mathstudent55
  • mathstudent55
The 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
  • mathstudent55
To find the slope, subtract the y-coordinates, and divide by the difference of the x-coordinates. Make sure you subtract the y-coordinates and the x-coordinates in the same order. Can you try this and tel me what you get?

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Lilmike234
  • Lilmike234
-1/2 ?
mathstudent55
  • mathstudent55
Correct. |dw:1437619975077:dw|
mathstudent55
  • mathstudent55
Notice 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
  • mathstudent55
Now that we have the slope, we do the next step.
mathstudent55
  • mathstudent55
The 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 y-coordinates, respectively, of a point on the line.
mathstudent55
  • mathstudent55
We 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
  • mathstudent55
All 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
  • mathstudent55
Let's use point (2, 3). We replace \(x_1\) with 2 and \(y_1\) with 3. \(y - 3 = -\dfrac{1}{2}(x - 2)\)
mathstudent55
  • mathstudent55
You already have the equation of the line. Now you can put the equation in standard form or slope-intercept form if you'd like to.
Lilmike234
  • Lilmike234
y=5/2x+8
Lilmike234
  • Lilmike234
?
mathstudent55
  • mathstudent55
\(y - 3 = -\dfrac{1}{2}(x - 2)\) \(2y - 6 = -(x - 2) \) \(2y - 6 = -x + 2\) \(2y = -x + 8\) \(y = -\dfrac{1}{2} x + 4\)
Lilmike234
  • Lilmike234
The answer choices are 1. y=5/2x+8 2. 5x+2y=16 3. 2x-3y=9 4. 5x-2y=16
mathstudent55
  • mathstudent55
Are you sure those are the choices of the same problem?
Lilmike234
  • Lilmike234
Yes
mathstudent55
  • mathstudent55
Can't be.
mathstudent55
  • mathstudent55
We have a slope of -1/2 None of those choices have a slope of -1/2
Lilmike234
  • Lilmike234
Well those were the answer choices
mathstudent55
  • mathstudent55
Let'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. 2x-3y=9 -3y = -2x + 9 y = 2/3 x - 3 slope 2/3 4. 5x-2y=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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