Answer:
In conclusion, the equation of the line parallel to x = 4 that passes through the point (11, 13) is y - 13 = ∞(x - 11).
Explanation:
To find the equation of a line parallel to the vertical line x = 4 and passing through the point (11, 13), we need to determine the equation of a line that has the same slope as the given line. Since the line x = 4 is vertical, it has an undefined slope. However, any vertical line will have a slope of infinity or negative infinity.
The equation of a vertical line is of the form x = a, where 'a' represents the x-coordinate of any point on the line. In this case, x = 4 represents the given vertical line. Since parallel lines have the same slope, any line parallel to x = 4 will also have an undefined slope.
To find the equation of a line passing through the point (11, 13) with an undefined slope, we can use the point-slope form of a linear equation. The point-slope form is given by:
y - y1 = m(x - x1),
where (x1, y1) represents a point on the line and 'm' represents the slope. In this case, since we have an undefined slope, we can substitute 'm' with infinity or negative infinity.
Using the point (11, 13), we can write the equation as:
y - 13 = ∞(x - 11).
Now, let's simplify this equation. Multiplying both sides by (x - 11), we get:
∞(x - 11)(y - 13) = ∞(x - 11) * ∞(x - 11).
Since infinity multiplied by any finite number is still infinity, we have:
∞(x - 11)(y - 13) = ∞.
This equation represents all possible lines parallel to x = 4 that pass through the point (11, 13). It indicates that for any value of (x - 11), y can take any value, resulting in an infinite number of lines parallel to x = 4 passing through (11, 13).