# Find the equation of the perpendicular straight line 2x-y + 5 = 0, passing through the points

Find the equation of the perpendicular straight line 2x-y + 5 = 0, passing through the points of intersection with the given straight line with the coordinate axes, respectively.

Let’s find the coordinates of the points of intersection of this straight line with the coordinate axes.

y = 0, so

2 * x – 0 + 5 = 0,

2 * x = – 5,

x = – 2.5, that is, the point of intersection with the abscissa axis has coordinates (-2.5; 0).

x = 0, so

2 * 0 – y + 5 = 0,

y = 5, that is, the point of intersection with the y-axis has coordinates (0; 5).

The equation of a straight line that passes through the point (-2.5; 0) and is perpendicular to this straight line will look like:

2 * (y – 0) – (-1) * (x + 2.5) = 0,

2 * y + x + 2.5 = 0 or 2 * x + 4 * y + 5 = 0.

The equation of the straight line that passes through the point (0; 5) and is perpendicular to this straight line will look like:

2 * (y – 5) – (-1) * (x – 0) = 0,

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