The graph of the linear equation [tex]y=2x[/tex] passes through which point?

(a) [tex](2,1)[/tex]
(b) [tex](2,-1)[/tex]
(c) [tex]\left(\frac{3}{2},-3\right)[/tex]
(d) [tex]\left(\frac{3}{2},3\right)[/tex]



Answer :

To determine which of the given points lies on the graph of the linear equation [tex]\( y = 2x \)[/tex], we'll substitute each point into the equation and verify if the equation holds true.

1. For point [tex]\((2, 1)\)[/tex]:
[tex]\[ \begin{align*} x &= 2 \\ y &= 1 \\ \end{align*} Substitute these values into the equation \( y = 2x \): \[ 1 = 2 \cdot 2 \implies 1 = 4 \][/tex]
This is not true. Therefore, point [tex]\((2, 1)\)[/tex] does not lie on the graph.

2. For point [tex]\((2, -1)\)[/tex]:
[tex]\[ \begin{align*} x &= 2 \\ y &= -1 \\ \end{align*} Substitute these values into the equation \( y = 2x \): \[ -1 = 2 \cdot 2 \implies -1 = 4 \][/tex]
This is not true. Therefore, point [tex]\((2, -1)\)[/tex] does not lie on the graph.

3. For point [tex]\(\left(\frac{3}{2}, -3\right)\)[/tex]:
[tex]\[ \begin{align*} x &= \frac{3}{2} \\ y &= -3 \\ \end{align*} Substitute these values into the equation \( y = 2x \): \[ -3 = 2 \cdot \frac{3}{2} \implies -3 = 3 \][/tex]
This is not true. Therefore, point [tex]\(\left(\frac{3}{2}, -3\right)\)[/tex] does not lie on the graph.

4. For point [tex]\(\left(\frac{3}{2}, 3\right)\)[/tex]:
[tex]\[ \begin{align*} x &= \frac{3}{2} \\ y &= 3 \\ \end{align*} Substitute these values into the equation \( y = 2x \): \[ 3 = 2 \cdot \frac{3}{2} \implies 3 = 3 \][/tex]
This is true. Therefore, point [tex]\(\left(\frac{3}{2}, 3\right)\)[/tex] lies on the graph.

Thus, the graph of the linear equation [tex]\( y = 2x \)[/tex] passes through the point [tex]\(\left(\frac{3}{2}, 3\right)\)[/tex]. The correct answer is:
(d) [tex]\(\left(\frac{3}{2}, 3\right)\)[/tex].