To determine where the line [tex]\( y = 3x - 2 \)[/tex] meets the [tex]\( y \)[/tex]-axis, you need to find the [tex]\( y \)[/tex]-intercept of the line.
The [tex]\( y \)[/tex]-intercept is the point where the line crosses the [tex]\( y \)[/tex]-axis. At this point, the value of [tex]\( x \)[/tex] is always zero because any point on the [tex]\( y \)[/tex]-axis has an [tex]\( x \)[/tex]-coordinate of zero.
To find the [tex]\( y \)[/tex]-intercept:
1. Set [tex]\( x = 0 \)[/tex] in the equation of the line.
2. Substitute [tex]\( x = 0 \)[/tex] into the equation [tex]\( y = 3x - 2 \)[/tex]:
[tex]\[
y = 3(0) - 2
\][/tex]
3. Simplify the expression:
[tex]\[
y = -2
\][/tex]
Therefore, the line [tex]\( y = 3x - 2 \)[/tex] meets the [tex]\( y \)[/tex]-axis at [tex]\( y = -2 \)[/tex]. The point where it intersects the [tex]\( y \)[/tex]-axis is [tex]\( (0, -2) \)[/tex].
