**Straight Line Problems With Solutions :**

Here we are going to see practical problems on straight line.

**Problem 1 :**

A photocopy store charges Rs. 1.50 per copy for the first 10 copies and Rs. 1.00 per copy after the 10th copy. Let x be the number of copies, and let y be the total cost of photocopying. (i) Draw graph of the cost as x goes from 0 to 50 copies. (ii) Find the cost of making 40 copies

**Solution :**

Here "x" stands for number of copies and "y" stands for total cost.

y = 1.5 x for 0 ≤ x ≤ 10

After 10th copy, we may pay Rs. 1.00 per copy

Let us construct a function for the number of copies which is greater than 10.

y = 1.5 (10) + 1 (x - 10)

y = 15 + x - 10

y = 5 + x for x > 10

(ii) Required cost for 40 copies

y = x + 5

y = 40 + 5

y = 45

**Problem 2 :**

Find atleast two equations of the straight lines in the family of the lines y = 5x + b, for which b and the x-coordinate of the point of intersection of the lines with 3x − 4y = 6 are integers

**Solution :**

Let us find the point of intersection of the above lines.

y = 5x + b ----(1)

3x − 4(5x + b) = 6

3x - 20x - 4b = 6

-17x - 4b = 6

-17x = 6 + 4b

x = -(6 + 4b)/17

The value of x will be either 17 or multiples of 17.

x = ±17, ±34,...............

-6 + 4b = 17 ==> b = -23/4

-6 + 4b = -17 ==> b = -11/4

Since "b" is integer, we cannot take these values.

-6 + 4b = 34 ==> b = 10

-6 + 4b = -34 ==> b = -7

5x - y + 10 = 0 and 5x - y - 7 = 0 are the required equations.

**Question 3 :**

Find all the equations of the straight lines in the family of the lines y = mx − 3, for which m and the x-coordinate of the point of intersection of the lines with x − y = 6 are integers.

**Solution :**

y = mx − 3 -----(1)

y = x - 6 -----(2)

mx - 3 = x - 6

x (m - 1) = 3

x = 3/(m - 1)

m - 1 = ±1 m - 1 = 1 m = 2 |
m - 1 = -1 m = 0 |
m - 1 = ±3 m - 1 = 3 m = 4 |
m - 1 = -3 m = -2 |

If m = 2, then y = 2x − 3

If m = 0, then y = − 3

If m = 4, then y = 4x − 3

If m = -2, then y = -2x − 3

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