Question 392244
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 = change in y/change in x}}}.

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 {{{4/1}}}, cancelling it out on the left side.  By multiplying the -1 on the right side by {{{4/1}}}, you get -4.
{{{-2-r = -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.
{{{-r = -2}}}
To isolate the variable, r, you divide both sides of the equation by -1.  That gives you the answer
{{{r = 2}}}

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.