# 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,

2 * y – 10 + x = 0 or x + 2 * y – 10 = 0.