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

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

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.

Approved by eNotes Editorial Team 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`

Approved by eNotes Editorial Team