Draw the graph of the equation 2x − 3y = 5. From the graph


Draw the graph of the equation 2x − 3y = 5. From the graph, find (i) the value of y when x = 4 and (ii) the value of x when y = 3.


Given equation :

$2 x-3 y=5$

$\Rightarrow 2 x=3 y+5$

$\Rightarrow x=\frac{3 y+5}{2}$

When, $y=-1, x=\frac{-3+5}{2}=\frac{2}{2}=1$

When, $y=-3, x=\frac{-9+5}{2}=\frac{-4}{2}=-2$

Thus, we have the following table:

Plot the points $(-2,-3),(1,-1)$ on the graph paper and extend the line in both directions.

(i) When x = 4:

$4=\frac{3 y+5}{2} \Rightarrow 8=3 y+5$

$\Rightarrow 3 y=8-5=3$

$\Rightarrow 3 y=3$

$\Rightarrow y=1$

(ii) When y = 3:

$x=\frac{3 y+5}{2}=\frac{14}{2}=7$

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