Question

If the point \[\left( {3,4} \right)\] lies on the graph of the equation \[3y = ax + 7\], find the value of \[a\].

Answer 1

Hint: Here, we will first use that if a point lies on the graph then it is a solution of the given equation, which is a value that makes the left hand side equal to the right hand side in the equation. So we will substitute the values of \[x\] and \[y\] in the given equation to find the required value.

Complete step-by-step answer:
We are given that the equation is
\[3y = ax + 7{\text{ ......eq(1)}}\]
We know that in a coordinate \[\left( {3,4} \right)\], where 3 is the value of \[x\] and 4 is the value of \[y\].
We also know that if a point lies on the graph of the equation then it is a solution of the equation, where a solution is a value we can put in place of a variable that makes the equation true, that is, the left hand side is equal to the right hand side in the equation.
Replacing 4 for \[y\] in the left hand side of the equation (1), we get
\[
   \Rightarrow 3\left( 4 \right) \\
   \Rightarrow 12 \\
 \]
Replacing 3 for \[x\] in the right hand side of the equation (1), we get
\[
   \Rightarrow a\left( 3 \right) + 7 \\
   \Rightarrow 3a + 7 \\
 \]
Since being a solution we have that the right hand side value of the equation is equal to the left side value \[ax + 7\] in the equation (1).
So we will take LHS equal to RHS to find the value of \[a\].
\[ \Rightarrow 12 = 3a + 7\]
Subtracting the above equation by 7 on both sides, we get
\[
   \Rightarrow 12 - 7 = 3a + 7 - 7 \\
   \Rightarrow 5 = 3a \\
 \]
Dividing the above equation by 3 on both sides, we get
\[
   \Rightarrow \dfrac{5}{3} = \dfrac{{3a}}{3} \\
   \Rightarrow \dfrac{5}{3} = a \\
   \Rightarrow a = \dfrac{5}{3} \\
 \]
Therefore, \[\dfrac{5}{3}\] is the value of \[a\].

Note: While solving these types of questions, students should know that if you are given the point on graph then it a solution of the given equation, which means that the left hand side is equal to the right hand side in the equation after substituting the value of the given variables. Students forget to check the answer, which can lead to the wrong answer. Avoid calculation mistakes.