Question

Student A states that the following two linear functions: 2x + 3y = 12 and 4x + 9 = 36 have the same slope, and therfore are parallel lines. Student B states that the lines are perpendicular, because the slopes are the inverse reciprocals of each other!

A) Student A is correct! The lines are parallel.
B) Student B is correct! The lines are perpendicular!
C) Both students are incorrect The lines intersect, but are not perpendicular!
D) Both students are correct!The lines are skewed!

Answer 1

C) Both students are incorrect The lines intersect, but are not perpendicular!

Explanation:

When the equations are in standard form, if the signs of the coefficients in one equation match those in the other, the lines cannot be perpendicular.

If the ratio of coefficients in one equation is different from the ratio of coefficients in the other equation, the lines cannot be parallel.

Here, the coefficients +2, +3 have the same signs and a different ratio than the coefficients +4, +9. Hence the lines intersect but are not perpendicular.