Final answer:
The line perpendicular to the y-axis passing through (-4,7) is the vertical line x = -4.
Step-by-step explanation:
The line that is perpendicular to the y-axis passes through the point (-4,7) is a vertical line that is parallel to the x-axis.
Since the given line is parallel to the x-axis, its equation can be written as x = -4. This means that for any value of y, x will always be -4.
For example, if we choose y = 5, the point (-4,5) will lie on the line. Similarly, if we choose y = -2, the point (-4, -2) will lie on the line as well.
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