Hi

Using the point-slope formula, 

 (r,4) and (-2,3)

Applying the point-slope formula***

 m = (3-4 ) /( -2-r) = 1/4

    |cross multiplying to solve for r

 (-2-r) = 4(3-4)

   -2-r = -4

     2 = r



CHECKING our Answer***

 -1/-4 = 1/4 

Answer by spikendb(5)   (Show Source): You can put this solution on YOUR website!
 Determine the value of r so that a line through the points with the coordinates (r,4) and (-2,3) has a slope of 1/4



To find r, you first have to plug the coordinates into .



m = slope



An easier formula to understand is m = y2-y1/x2-x1

You plug in the coordinates to have:

1/4 = 3-4/-2-r



Then you have to solve the formula for r.



1/4 = 3-4/-2-r

You subtract 4 from 3 to get -1

1/4 = -1/-2-r

Next, you multiply both sides of the equation by -2-r/1

By multiplying both sides by -2-r/1, you cancel out the -2-r on the right side, and move it to the left.  Only -1 remains on the right side of the equation.

1/4(-2-r) = -1

You multiply both sides of the equation by , cancelling it out on the left side.  By multiplying the -1 on the right side by , you get -4.



You add 2 to both sides of the equation.  It cancels it out on the left side, and creates a -2 on the right side.



To isolate the variable, r, you divide both sides of the equation by -1.  That gives you the answer





You can check your answer by plugging 2 in for r in the original equation:

1/4 = 3-4/-2-2

1/4 = -1/-4

1/4 = 1/4

The answer to the problem is r = 2. 

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