ALGEBRA HELP pleasee (:?

Your last sentence carries no meaning. However if your question requires " finding out the value of ' r ' when the slope of the line = 5/8, Then, here is the solution -

The slope of the line m = ( y2 - y1 ) / ( x2 - x1 ). In our case --

y1 = r, y2 = 6, , x1 = 5, and x2 = r,

Substituting these values in the above mentioned formula we get ----

5/8 = ( 6 - r ) divided by ( r - 5 )

=> ( 6 - r ).8 = ( r - 5 ) .5

=> 48 - 8.r = 5.r - 25

=> 48 + 25 = 5.r + 8.r

=> 13.r = 73

=> r = 73/13 = 5 . 6 1 5 ........... Answer Answer

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CHECK

Substitute r = 73/13 in eqn (1) –

=> ( 6 – r ) / ( r – 5 ) = ( 6 - 73/13 ) / (73/13 - 5 )

= [ (78-73)/13 ] divided by [ (73 – 65) / 13 ]

= ( 5/13 ) / (8/13)

= 5/8 …………………. Which is the slope (given value)

Hence value of r = 73/13 is correct .

For the slope to be 5/8, (6 - r) / (r - 5) must equal 5/8 (the rise over the run is 5/8).

(6 - r) / (r - 5) = 5/8

Cross-multiply:

5(r - 5) = 8(6 - r)

Multiply it out:

5r - 25 = 48 - 8r

Add 8r to both sides:

5r - 25 + 8r = 48 - 8r + 8r

or

13r - 25 = 48

Add 25 to both sides:

13r = 73

Divide both sides by 13:

r = 73/13

The points will be (5, 73/13) and (73/13, 6)

Check:

Rise: 6 - 73/13 or 78/13 - 73/13 = 5/13

Run: 73/13 - 5 or 73/13 - 65/13 = 8/13

Slope: (5/13) / (8/13)

Invert and multiply:

(5/13) * (13/8) = 5/8