The following observed value of x and y are thought to satisfy a linear equation. Write the linear equation-

Draw the graph using the value of x, y as given in the above table.

At what points the graph of the linear equation

(i) cuts the X-axis ?

(ii) cuts the Y-axis?

The linear equation for the line will be-

y = mx + c

Where, c is the y-intercept, which from the graph is 2.

⇒ c = 2.

Taking x₁ = 6, y₁ = – 2 and x₂ = – 6, y₂ = 6

Now, m = slope of the line

∴ the linear equation will be-

⇒ 3y = – 2x + 6 (multiplying whole equation by 3)

⇒ 2x + 3y – 6 = 0

Now, the point where graph cuts:

(i)x-axis

For this, y = 0.

∴putting x = 0 in 2x + 3y – 6 = 0, we get-

⇒ 2x + 3×0 – 6 = 0

⇒ 2x = 6

⇒ x = 3

∴ the point where graph cuts x-axis is(3, 0).

(ii) y-axis

For this, x = 0.

∴putting x = 0 in 2x + 3y – 6 = 0, we get-

⇒ 2×0 + 3y – 6 = 0

⇒ 3y = 6

⇒ y = 2

∴ The point where graph cuts y-axis is (0, 2).