System of Straight Lines

Find the angle between the lines whose slopes are `1/2` and 3.

Find the distance of the point (4, 1) from the line 3x – 4y + 12 = 0.

Show that the straight lines x + y – 4 = 0, 3x + 2 = 0 and 3x – 3y + 16 = 0 are concurrent.

Find the value of ‘a’ for which the straight lines 3x + 4y = 13; 2x – 7y = -1 and ax – y – 14 = 0 are concurrent.

A manufacturer produces 80 TV sets at a cost of ₹ 2,20,000 and 125 TV sets at a cost of ₹ 2,87,500. Assuming the cost curve to be linear, find the linear expression of the given information. Also, estimate the cost of 95 TV sets.

As the number of units produced increases from 500 to 1000 and the total cost of production increases from ₹ 6000 to ₹ 9000. Find the relationship between the cost (y) and the number of units produced (x) if the relationship is linear.

Prove that the lines 4x + 3y = 10, 3x - 4y = - 5 and 5x + y = 7 are concurrent.

Find the value of p for which the straight lines 8px + (2 - 3p)y + 1 = 0 and px + 8y - 7 = 0 are perpendicular to each other.