Final answer:
The equation for a line perpendicular to the y-axis passing through (4,7) is x = 4.
Step-by-step explanation:
The student is asking for the equation of a line in slope-intercept form that is perpendicular to the y-axis and passes through the point (4,7). A line perpendicular to the y-axis is a vertical line. Since the slope-intercept form is y = mx + b, where m is the slope, for a vertical line, the slope is undefined and the equation cannot be expressed in slope-intercept form.
However, the equation for a vertical line is simply x equals the x-coordinate of any point on the line. Therefore, the equation for a line perpendicular to the y-axis passing through (4,7) is x = 4.