Draw the graph obtained from the table below :

x	a	3	-5	5	c	-1
y	-1	2	b	3	4	0

Use the graph to find the values of a, b and c. State a linear relation between the variables x and y.

Plot the given points (3, 2), (5, 3) and (-1, 0) on a graph paper.

Draw a straight line passing through these points.

To find the value of 'a':

Through y = -1, draw a horizontal line which meets the graph at a point, say P. Through P, draw a vertical line which meets the x-axis at x = -3.

∴ a = -3

To find the value of 'b':

Similarly, through x = -5, draw a vertical line which meets the graph at a point, say Q. Through Q, draw a horizontal line which meets the y-axis at y = -2.

∴ b = -2

To find the value of 'c':

Similarly, through y = 4, draw a horizontal line which meets the graph at a point, say R. Through R, draw a vertical line which meets the x-axis at x = 7.

∴ c = 7

Let the linear relation between the variable x and y be y = mx + c.

Since, the graph passes through the point (3, 2); substitute x = 3 and y = 2 in y = mx + c.

This gives 2 = 3m + c ……………(1)

Again, the graph passes through the point (5, 3); substitute x = 5 and y = 3 in y = mx + c

This gives 3 = 5m + c ……………(2)

Subtracting (2) from (1),

2 - 3 = 3m + c -5m - c

⇒ -1 = -2m

⇒ m = $\dfrac{1}{2}$

Substituting the value of m in equation (1),

2 = 3 $\times \dfrac{1}{2}$ + c

⇒2 = $\dfrac{3}{2}$ + c

⇒2 - $\dfrac{3}{2}$ = c

⇒ $\dfrac{4}{2} - \dfrac{3}{2}$ = c

⇒ c = $\dfrac{1}{2}$

∴ Required relation is : y = mx + c i.e. x = 2y - 1

Hence, a = -3, b = -2 and c = 7. Linear relation : x = 2y - 1.