The options that represent the front side of the deck, which is perpendicular to the left side with the equation 3x−2y=10, are B, D, and E.
How do we find the equations perpendicular to the left side?
A. .
6x−4y=2 ⇒ y= 3/2x - 1/2. The slope is 3/2, which is not the negative reciprocal of 3/2. So, this is not correct.
B.
4x+6y = 12 ⇒ y = -2/3x + 2. . The slope is −2/3 is the negative reciprocal of 3/2. This is a correct option.
C.
x = - 6/9y + 4 ⇒ x = -2/3x + 4. Simplifying the coefficient of x gives a slope of −3/2, not −2/3.
D.
2x + 3y = 7 ⇒ y = −2/3x + 7/3. The slope is −2/3, which is the negative reciprocal of 3/2.
E.
−2x = 3y ⇒ y = −2/3x. The slope is −2/3, which is the negative reciprocal of 3/2.