Make an equation of the straight lines passing through the point A (5; 1) parallel and perpendicular

Make an equation of the straight lines passing through the point A (5; 1) parallel and perpendicular to the straight line 2x-5y + 3 = 0.

2x – 5y + 3 = 0.

Let us bring the equation to the standard form:

5y = 3 + 2x.

y = 2 / 5x +3/5.

1) The slope is 2/5. A parallel line will have the same slope.

The straight line equation has the form y = kx + b.

The parallel line equation will be y = 2 / 5x + b.

Since the straight line passes through point A (5; 1) (x = 5, y = 1), then we calculate the value of b.

1 = 2/5 * 5 + b;

2/5 * 5 + b = 1;

2 + b = 1;

b = -1.

Parallel line equation: y = 2 / 5x – 1.

2) y = 2 / 5x +3/5. The slope is 2/5. A perpendicular line will have a slope (-5/2 = -2.5).

The equation of the perpendicular line will be y = -2.5x + b.

Since the straight line passes through point A (5; 1) (x = 5, y = 1), we calculate the value of b.

1 = -2.5 * 5 + b;

-2.5 * 5 + b = 1;

-12.5 + b = 1;

b = 13.5.

Perpendicular line equation: y = -2.5x + 13.5.