Question

Analyzing Student Work
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.

Answer 1

The error is in the step used to isolate y.

Start correctly:
y - (−8) = −6(x − 2)
y + 8 = −6x + 12

To solve for y you must subtract 8 from both sides, not add 8. Subtracting 8 gives
y = −6x + 12 − 8
y = −6x + 4.

(The student instead added 8 to both sides, producing y = −6x + 20, which is wrong. Check: plugging x = 2 into y = −6x + 4 gives y = −12 + 4 = −8, the given point; plugging into y = −6x + 20 gives y = 8, not −8.)