Find the slope-point form of the equation of a line perpendicular to the y-axis through (4,1).
a line perpendicular to the y-axis has slope 0
so, since it goes through (4,1), the line is just
y-1 = 0(x-4)
or,
y = 1
To find the slope-point form of the equation of a line perpendicular to the y-axis through a given point, we need to determine the equation of the line first. Since the line is perpendicular to the y-axis, it will be a vertical line, and all vertical lines have the equation x = a, where 'a' is the x-coordinate of any point on that line. In this case, the line passes through (4,1), so the equation will be x = 4.
Now, let's write the slope-point form of the equation of a line. The slope-point form is given by y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and 'm' is the slope of the line. Since the given line is vertical, its slope is undefined.
In this case, the line x = 4 does not have a defined slope. Therefore, it cannot be expressed in the slope-point form.
Alternatively, if you were asked for the point-slope form of the equation, it would be y - y₁ = 0(x - x₁), because the slope of a vertical line is undefined. In this case, the equation would simplify to y - 1 = 0, or y = 1.