The slope intercept formula is "y = mx + b where "m" is the slope and "b" represents the "y" value of the "y" intercept point.

In your case, 

m = -2

so the eqaution is y = -2x + b.

We also know that the points (-5,10) and (r,-12) lie on y = -2x + b so

For x = -5, y = 10 that is:

10 = -2*(-5) + b

-2*(-5) + b = 10

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Click here to see step by step solution for b

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b = 0

No we know the equation for the line is

y = 2x

and also that (r,-12) lies on the line, meaning

For x = r, y = -12, meaning, if we plug in the values into y = 2x we will get:

-12 = 2r

2r = - 12

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Click here to see the step by step solution

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r = -6