If the point $(3, \,4)$ lies on the graph of the equation $3y = ax + 7$, find the value of $a$.
If the point $(3, \,4)$ lies on the graph of the equation $3y = ax + 7$, find the value of $a$.
The equation of the given line is. $3 y= ax +7$
$\because \,\,\,(3,\,4)$ lies on the given line.
$\therefore $ It must satisfy the equation $3 y = ax +7$
We have $(3,\,4) \Rightarrow x=3$ and $y=4$
L.H.S. $=3 y$ R .H.S. $= ax +7$
$=3 \times 4$ $=a \times 3+7$
$=12$ $=3 a+7$
$\because $ L.H.S. $=$ R.H.S.
$\therefore $ $12=3 a+7$
or $3 a=12-7=5$
or $a=\frac{5}{3}$
Thus, the required value of a is $\frac{5}{3}$.
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For each of the graphs given in Fig. select the equation whose graph it is from the choices given below :
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