Question

The graph of $2x + y = 3$ passes through the origin. Is this statement true or false?
A) True
B) False

Answer 1

Hint:
As it is given that the graph of the given passes through the origin and we have to check that statement. If any point lies on the graph then it must satisfy the equation of the graph i.e. when we put that point in the equation, we get the value as zero. So we will put the point of origin in the given equation and if we get the value as zero then it lies on the graph otherwise not.

Complete step by step solution:
The given equation is $2x + y = 3$.
We know that if the point satisfies the equation, then the graph passes through that point.
As we know the point of origin is $\left( {0,0} \right)$
Now, we will substitute the value of $x$ as 0 and value of $y$ as 0 in the equation.
$ \Rightarrow 2 \cdot 0 + 0 = 3$
On further simplification, we get
$ \Rightarrow 0 = 3$
This is not possible. We can say that the point is not satisfying the equation of line.
Hence, the given statement i.e. the graph of $2x + y = 3$ passes through the origin is false.

Hence, the correct option is option B.

Note:
Remember that if any point lies on the given line then it would satisfy the equation of line. To check whether a point lies on the given line, we should always substitute the value of x-coordinate in place of \[x\] and y-coordinate in place of \[y\]. If we get the value of left hand side of equation equal to the right hand side of equation, then the given point will lie on the line and if we get the value of left hand side of equation not equal to the value of the right hand side of the equation, then the given point will not lie on the line.