Right this is pretty simple all you do is sub the points to the equation given.
So first try the first point (2,-1) in y=-3x+7
==> -1=-3(2)+7
==>-1=1 this is not equal therefore not the right points
Then try (1,10)
==>10=-3(1)+7
==>10=4 this is incorrect therefore not the right points
Next try (3,-2)
==>-2=-3(3)+7
==>-2=-2 this is equal therefore this is the coordinates to the linear equation.
Finally try the last points to make sure you are correct.
==> -8=-3(-5)+7
==>-8=22 this is incorrect also.
Therefore the only coordinates that satisfies the equation is (3,-2)
C is the correct answer because that's the only answer where all the numbers (i.e. 3, -1, 2) all, when plugged into the function, equal 0. For example:
3³ - (4 × 3²) + 3 + 6 = 0
-1³ - (4 × (-1)²) + (-1) + 6 = 0
2³ - (4 × 2²) + 2 + 6 = 0
As we see, everything adds up to 0. So, C is the correct answer.
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D=√(0.9²+2.5²)=2.65
The distance between two points is 2.65