# STRAIGHT LINE PROBLEMS WITH SOLUTIONS

## About "Straight Line Problems With Solutions"

Straight Line Problems With Solutions :

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

## Straight Line Problems With Solutions - Practice questions

Question 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 ≤ ≤ 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

Question 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  =  ±1m - 1  =  1m = 2 m - 1  =  -1m = 0 m - 1  =  ±3m - 1  =  3m  =  4 m - 1  =  -3m  =  -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 After having gone through the stuff given above, we hope that the students would have understood "Straight Line Problems With Solutions".

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