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  • The following observed values of x and y are thought to satisfy a linear equation. Write the linear equation :

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

x 6 -6
y -2 6

Draw the graph using the values 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

Answers (1)

Let the linear equation is y = mx + c … (i), and it satisfies the points (6, –2), (–6, 6)

So, we have:

–2 = 6m + c … (ii)

6 = – 6m + c …(iii)

Adding equation (ii) & (iii) we get

4 = 2c

\frac{4}{2}=c

c = 2

On putting the value of c = 2 in equation (ii) we get

–2 = 6 m + 2

– 2 – 2 = 6 m

–4 = 6 m

-\frac{4}{6}=m

m=-\frac{2}{3}

Now, equation (i) becomes y=-\frac{2}{3}x+2

which gives

3y + 2x = 6 … (iv)

Which is required equation and its graph is

Putting y = 0 in equation (iv), we get

2x = 6

x = 3

Hence the graph cut x-axis at (3, 0)

Putting x = 0 in equation (iv), we get

3y = 6

y = 2

Hence the graph cut y axis at (0, 2)

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