Linear functions

Question

Is the equation y = 3x + 1 parallel, perpendicular, or neither to - 3 x + y = 7 ?

Answer 1

-3x + y = 7

y = 3x + 7

With matching slopes of 3 and different y-intercepts, we have parallel lines.

Perpendicular lines have opposite, reciprocal slopes. A line perpendicular to our given lines would have a slope of -1/3.

A slope of neither 3 or -1/3 would be neither parallel nor perpendicular.

Answer 2

Parallel lines have the SAME SLOPE. Equation 1 has slope of 3, Equation 2 has slope of -3, so NOT parallel.

Perpendicular lines have "opposite reciprocal" (flip the fraction, change the sign) slopes. Equation 1 has slope 3, its opposite reciprocal would be -1/3, so Equation 2 does not have that slope. So they are NOT perpendicular.

So they are neither.