Find the equation of the straight line passing through the origin and through the point of intersection of the lines 5x + 7y = 3 and 2x - 3y = 7.

State which one of the following is true :
The straight lines y = 3x - 5 and 2y = 4x + 7 are

(i) parallel

(ii) perpendicular

(iii) neither parallel nor perpendicular.

If the straight lines 3x - 5y + 7 = 0 and 4x + ay + 9 = 0 are perpendicular to one another, find the value of a.

If the lines 3x + by + 5 = 0 and ax - 5y + 7 = 0 are perpendicular to each other, find the relation connecting a and b.