Find the equation of the line containing the points (-2,3) and (2,-3).

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

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The equation of a line with the points (x1, y1) and (x2, y2) is given by (y - y1)/(x - x1) = (y2 - y1)/(x2 - x1)

We have to find the line with the points (-2, 3) and (2, -3).

The equation of the line is (y + 3)/(x - 2) = (3 + 3)/(-2 - 2)

=> (y + 3)/(x - 2) = 6/(-4)

=> (y + 3)/(x - 2) = -3/2

=> 2*(y + 3) = -3*(x - 2)

=> 2y + 6 = -3x + 6

=> 2y + 3x = 0

The line with the points (-2, 3) and (2, -3) is 3x + 2y = 0

iislas104's profile pic

iislas104 | High School Teacher | (Level 1) eNoter

Posted on

Step 1: Find the slope from the two points given to you by using the formula  Slope (m) = (y2 –y1)/( x2 – x1)

     x1=-2, y1=3,   x2=2,  y2=-3  so m= (-3 –3)/( 2– -2)=-6/4=-3/2

Step2: Find the y-intercept (b) using the slope-intercept form(y=mx+b)

    Chose one the point to sub for your x and y (I will choose the first point) so xà -2 and y à 3 and of course you just solved for the slope so you now know m à -3/2          

   Y =    m    x     + b

   3 = (-3/2)( -2) + b    Now solve the equation for b

   3 =         3      +   b

  0  =     b 

Step 3: Now you know both m(slope) and b(y-intercept) so you can write the equation as

                          y=(-3/2) x + 0     OR     y=(-3/2) x    

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