Question 1047189
The basic idea is to use the slope formula to solve for r. I show how to do this below



Step 1) {{{m = (y[2]-y[1])/(x[2]-x[1])}}}



Step 2) {{{-3 = (r-(-2))/(4-6)}}}



Step 3) {{{-3 = (r+2)/(4-6)}}}



Step 4) {{{-3 = (r+2)/(-2)}}}



Step 5) {{{-2*(-3) = -2*((r+2)/(-2))}}}



Step 6) {{{6 = r+2}}}



Step 7) {{{r+2 = 6}}}



Step 8) {{{r+2-2 = 6-2}}}



Step 9) {{{r = 4}}}



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The explanation for each step is given here



Step 1) Start with the slope formula



Step 2) Plug in the given information



Step 3) Rewrite {{{r-(-2)}}} as {{{r+2}}}



Step 4) Simplify {{{4-6}}} to get {{{-2}}}



Step 5) Multiply both sides by -2 (to undo the division of -2)



Step 6) Multiply and simplify. Notice how the "-2" terms cancel on the right side



Step 7) Flip the equation



Step 8) Subtract 2 from both sides (to undo the addition of 2)



Step 9) Combine like terms



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The final answer is {{{r = 4}}}