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Write the point-slope form of an equation for the line passing through the point at...

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tipha | Student, Grade 9 | (Level 2) eNoter

Posted October 22, 2011 at 6:33 AM via web

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Write the point-slope form of an equation for the line passing through the point at (3,-6) with slope -4/3.

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Matthew Fonda | eNotes Employee

Posted October 22, 2011 at 7:00 AM (Answer #1)

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Use the point-slope equation:

`y - y_1 = m(x - x_1)`

We're given x = 3, y = -6, and m = -4/3. Let's plug them into the point-slop equation:

`y - -6 = -4/3(x - 3)`

We then simplify:

`y + 6 = -4/3 x + 4`

We then solve for y to obtain our solution:

`y = -4/3x - 2`

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dpaden | Elementary School Teacher | (Level 1) Adjunct Educator

Posted October 22, 2011 at 7:32 AM (Answer #2)

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The point slope formula is `y-y' = m(x-x')` where m is the slope and x' and y' are the values of one of the points.

To find the slope you need to know the rise (change in the value of y) and the value of the run (the change in the value of x).  The slope is rise / run.  y changed from -6 to 3 or a change of +9.  x changed from 3 to -4 or a change of -7.

`(Delta y)/(Delta x)` = `(+9)/-7` = `(rise)/(run)` = slope = m


Using this value for m and the point 3, -6 we get-

` `` `` <strong>y-(-6) = -9/7(x-3)</strong> `` `` `

` ` `y+6 = -9/7x+9/7*3`

`y = -9/7`x -2 1/7

Test: Use the other point  y=3 and x=-4

`3 = -9/7(-4) - 2 1/7`

`3 = 36/7 - 15/7` = 21/7 = 3  The equation works.

 

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patelmilia98 | Student, Grade 9 | (Level 1) Valedictorian

Posted October 22, 2011 at 6:34 AM (Answer #3)

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i think it's 3x+-6=14

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