Use the graphical method to find the value of k, if :

(i) (k, -3) lies on the straight line 2x + 3y = 1

(ii) (5, k - 2) lies on the straight line x - 2y + 1 = 0

(i) 2x + 3y = 1

Step 1:

Give at least three suitable values to the variable x and find the corresponding values of y.

Let x = 0, then 2 $\times$ 0 + 3y = 1 ⇒ y = 0.3

Let x = 2, then 2 $\times$ 2 + 3y = 1 ⇒ y = -1

Let x = 4, then 2 $\times$ 4 + 3y = 1 ⇒ y = -2.3

Step 2:

Make a table (as given below) for the different pairs of the values of x and y:

Step 3:

Plot the points, from the table, on a graph paper and then draw a straight line passing through the points plotted on the graph.

Since, point (k, -3) lies on the straight line drawn, through y = -3, draw a horizontal line which meets the straight line at point, say Q. Through point Q, draw a vertical line which meets the x-axis at 5.

Hence, the value of k = 5.

(ii) x - 2y + 1 = 0

Step 1:

Give at least three suitable values to the variable x and find the corresponding values of y.

Let x = -1, then -1 - 2y + 1 = 0 ⇒ y = 0

Let x = 0, then 0 - 2y + 1 = 0 ⇒ y = 0.5

Let x = 1, then 1 - 2y + 1 = 0 ⇒ y = 1

Step 2:

Make a table (as given below) for the different pairs of the values of x and y:

Step 3:

Plot the points, from the table, on a graph paper and then draw a straight line passing through the points plotted on the graph.

Since, point (5, k - 2) lies on the straight line drawn, through x = 5, draw a vertical line which meets the graph at a point, say Q. Through point Q, draw a horizontal line which meets the y-axis at point 3.

k - 2 = 3

⇒ k = 3 + 2

⇒ k = 5

Hence, the value of k = 5.