Question

Question 2
The following observed values of x and y are thought to satisfy a linear equation. Write the linear equation.
$\begin{array}{ccc}X& 6& -6\\ Y& -2& 6\end{array}$
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?

Answer 1

Given points are (6, -2) and (-6, 6).
Let the linear equation y = mx + c is satisfied by the points (6, - 2) and (-6, 6).
At point (6, -2),
-2 = 6m + c ……(i)
And, at point (-6, 6); 6 = -6m + c ….(ii)
Solving the equations (i) and (ii) we get,

$6m+c=-2$
$-6m+c=6$
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$0+2c=4$
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$\Rightarrow [c=2]$

Substituting c = 2 in eq (i)

$\Rightarrow 6m+2=-2$
$\Rightarrow 6m=-2-2$
$\Rightarrow 6m=-4$
$\Rightarrow m=\frac{-4}{6}$
$\Rightarrow [m=\frac{-2}{3}]$

On putting $m=-\frac{2}{3}$ and $c=2$ in linear equation
$y=mx+c$ , we get


$\Rightarrow y=-\frac{2}{3}x+2\Rightarrow y=\frac{-2x+6}{3}\Rightarrow 3y=-2x+6$

When the graph of the linear equation,

(i) Cuts the x-axis
Then, put y = 0 in equation 2x + 3y = 6; we get,
$\Rightarrow 2x+3.0=6$
$\Rightarrow 2x=6$
$\therefore x=3$

When the graph of the linear equation,

(ii) Cuts the y-axis
Then, put x = 0 in equation 2x + 3y = 6; we get,
$\Rightarrow 2.0+3y=6$
$\Rightarrow 3y=6$
$\therefore y=2$

Therefore, the graph of the linear equation cuts the x-axis at the point (3, 0) and the y-axis at the point (0, 2).