Question:
If the point (3, 4) lies on the graph of 3y = ax + 7 then the value of a is
(a) $\frac{2}{5}$
(b) $\frac{5}{3}$
(c) $\frac{3}{5}$
(d) $\frac{2}{7}$
Solution:
Given equation: $3 y=a x+7$.
Also, $(3,4)$ lies on the graph of the equation.
Putting $x=3, y=4$ in the equation, we get:
$3 \times 4=3 a+7$
$\Rightarrow 12=3 a+7$
$\Rightarrow 3 a=12-7=5$
$\Rightarrow a=\frac{5}{3}$
Hence, the correct answer is option (b).