A student writes the equation for a line that has a slope of
-6 and passes through the point (2,8).
y-(-8)= -6(x - 2)
y-(-8)= -6x + 12
y-(-8) + 8 = -6x + 12 + 8
y=-6x + 20
Explain why the work is not correct.

Step-by-step explanation:

The point-slope form of the equation of a line is ...

  y -k = m(x -h)

for a point (h, k) and a slope m.

The problem statement tells us m=-6 and (h, k) = (2, 8). Putting these values into the form gives ...

  y -8 = -6(x -2)

The first line of "the work" uses -8 instead of 8. We cannot tell if that is an error in the work, or a typo in the problem statement. Either way, they disagree.

__

The last line of "the work" adds -(-8) and +8 to give a result of 0. That is definitely an error, regardless of the above.

_____

Comment on the result

If the problem statement has no typo, the errors cancel and the student ended up with the right equation.

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