Which pair of equations describes the line through $(3, -1, 2)$ parallel to the $y$ -axis?

y = -1

and

z = 2

Correct answerYour answer

x = 3

and

y = -1

Correct answerYour answer

x = 3

and

z = 2

Correct answerYour answer

x = 0

and

z = 0

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

Parallel to the $y$ -axis means direction ratios $0, 1, 0$ : $\frac{x - 3}{0} = \frac{y + 1}{1} = \frac{z - 2}{0}$ .
The zero denominators mean $x$ and $z$ never change along the line: $x = 3$ and $z = 2$ , with $y$ free.

Worth noting

$y = -1$ and $z = 2$ fixes $y$ , the one coordinate that changes along a line parallel to the $y$ -axis.

Ten questions from Three-Dimensional Geometry, at your own pace.

Which pair of equations describes the line through (3,−1,2)(3, -1, 2)(3,−1,2) parallel to the yyy-axis?