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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mfonda's profile pic

Matthew Fonda | eNotes Employee

Posted on

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 on

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.

 

patelmilia98's profile pic

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

Posted on

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

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