Question

Alejandro made an error in the steps below when determining the equation of the line that is perpendicular to the line 4x – 3y = –8 and passes through the point (3, –2).



Alejandro made his first error in which step?

Step 1
Step 2
Step 3
Step 4

Answer 1

I don’t see the four steps you mention — could you paste them (or upload a picture)? I can’t tell which is the first error without seeing his work.

Meanwhile, here are the correct steps and final answer so you can compare to Alejandro’s work:

Correct steps
1. Put 4x − 3y = −8 into slope-intercept form: −3y = −4x − 8, so y = (4/3)x + 8/3. The slope of the given line is 4/3.
2. The slope of a perpendicular line is the negative reciprocal: −3/4.
3. Use point–slope with point (3, −2): y + 2 = (−3/4)(x − 3).
4. Solve for y: y + 2 = (−3/4)x + 9/4 → y = (−3/4)x + 9/4 − 2 = (−3/4)x + 1/4.

So the perpendicular line is y = (−3/4)x + 1/4.

If Alejandro’s work differs from these, his first error is whichever step first deviates from the above (for example, an incorrect slope in Step 1 or an algebra mistake in Step 4). Paste his four steps and I’ll point out the exact first error.