SAT Math online in Paris: find the slope of a perpendicular line
A coordinate problem may require two linked decisions: finding the first line’s slope and interpreting how another line relates to it. Solving only the first step can produce a plausible answer to a different question.
Original teaching problem
In the coordinate plane, one line passes through (2, 5) and (6, 13). A second line is perpendicular to it and passes through (2, 5). What is the slope of the second line?
This is an original exercise, not an official SAT item. The SAT’s Math content includes linear functions and geometric relationships; identify the required skill from the question rather than assuming a score reveals a particular topic weakness.
Calculate the first slope consistently
The change in y is 13 − 5 = 8, and the corresponding change in x is 6 − 2 = 4. The first slope is 8/4 = 2. Use the same point order in numerator and denominator.
For two perpendicular lines with defined, nonzero slopes, their slopes multiply to −1. If the second slope is m, then 2m = −1. Therefore m = −1/2.
Distinguish common wrong answers
- 2 is the slope of the first line, not the perpendicular line.
- −2 changes the sign but does not take the reciprocal.
- 1/2 takes the reciprocal but misses the sign change.
The product check confirms the answer: 2 × (−1/2) = −1.
Use the point for an optional equation check
The point (2, 5) is not needed to determine the perpendicular slope once the first slope is known. It identifies which perpendicular line is intended. Its equation can be written as y − 5 = −(1/2)(x − 2), or y = −x/2 + 6. Substituting x = 2 returns y = 5.
Do not apply the reciprocal formula blindly to a horizontal line: its perpendicular is vertical and has an undefined slope. State the conditions under which a rule applies.
Choose follow-up practice from your actual attempt
If the first slope was wrong, review differences and point order. If the first slope was correct but the second was wrong, focus on perpendicular relationships. Try a fresh problem to check that the correction transfers.
The free Math Skills Check offers more original practice. For online SAT support from Paris, bring the working that led to your answer so the lesson can address the specific step.