Equation;
x=y-4
x-y+4=0

x-y+4 will be the equation for (-1,3)
and
it will neither pass from y-axis not from x-axis

Parallel to x-axis:
When a line is parallel to the x-axis, it means that the line has a constant y-coordinate and any change in the x-coordinate does not affect the y-coordinate. In other words, the line is horizontal and its slope is 0.

To find the equation of a line parallel to the x-axis passing through the point (-1,3), we can use the general form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.

Since the line is parallel to the x-axis and has a slope of 0, the equation becomes y = 0x + b. Simplifying further, we get y = b.

Since the line passes through the point (-1,3), we can substitute the coordinates into the equation to find the value of b.

3 = b

Therefore, the equation of the line parallel to the x-axis passing through (-1,3) is y = 3.

Parallel to y-axis:
When a line is parallel to the y-axis, it means that the line has a constant x-coordinate and any change in the y-coordinate does not affect the x-coordinate. In other words, the line is vertical and its slope is undefined.

To find the equation of a line parallel to the y-axis passing through the point (-1,3), we can use the general form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.

Since the line is parallel to the y-axis and has an undefined slope, the equation becomes x = b.

Since the line passes through the point (-1,3), we can substitute the coordinates into the equation to find the value of b.

-1 = b

Therefore, the equation of the line parallel to the y-axis passing through (-1,3) is x = -1.

Neither parallel to x-axis nor y-axis:
To find the equation of a line that is neither parallel to the x-axis nor y-axis passing through the point (-1,3), we need to find the slope of the line.

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula: m = (y2 - y1) / (x2 - x1).

Let's consider another point (x, y) on the line. Since the line is neither parallel to the x-axis nor y-axis, the slope will be non-zero and finite.

Using the slope formula, we have:

m = (y - 3) / (x - (-1))

Since the line is not parallel to the x-axis, the denominator (x - (-1)) cannot be zero. Therefore, x ≠ -1.

To find the equation of the line passing through (-1,3) with a non-zero and finite slope, we need to know the value of x.

Therefore, the equation of the line that is neither parallel to the x-axis nor y-axis passing through (-1,3) cannot be determined without additional information.