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The equation of the line that passes through the point \(\left(\frac{4}{3}, -2\right)\) and is parallel to the y-axis is:

\[
x = \frac{4}{3}
\]

The plot above shows this vertical line in blue, and the red point represents \(\left(\frac{4}{3}, -2\right)\), through which the line passes.

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Here are five related questions to explore:

1. What is the equation of a line parallel to the x-axis passing through a point?
2. How would the equation change if the line were perpendicular to the y-axis?
3. Can we express vertical lines in slope-intercept form \(y = mx + b\)? Why or why not?
4. How do you determine the slope of a line parallel to the y-axis?
5. What is the equation of a line passing through \(\left(1, -3\right)\) and parallel to the y-axis?

**Tip:** Vertical lines always have undefined slopes because their change in x is zero, which leads to division by zero when calculating the slope.

Find the equation of the line through (4/3, -2) parallel to the y-axis.

Discover how to find the equation of a line that passes through the point (4/3, -2) and is parallel to the y-axis. This problem explains key concepts like vertical lines, undefined slopes, and linear equations in coordinate geometry. Perfect for students in Grades 7-9.

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