Question

Draw the graph of y=2x+1 ,y= 2x and y=2x-1/2 are these parallel

Answer 1

$\large\underline{\sf{Solution-}}$

Consider,

$\red{\rm :\longmapsto\:y = 2x + 1}$

Substituting 'x = 0' in the given equation, we get

$\red{\rm :\longmapsto\:y = 0 + 1}$

$\red{\rm :\longmapsto\:y = 1}$

Substituting 'x = 1' in the given equation, we get

$\red{\rm :\longmapsto\:y = 2 + 1}$

$\red{\rm :\longmapsto\:y = 3}$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 1 \\ \\ \sf 1 & \sf 3 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points

➢ See the attachment graph.

Consider,

$\blue{\rm :\longmapsto\:y = 2x}$

Substituting 'x = 0' in the given equation, we get

$\blue{\rm :\longmapsto\:y = 2 \times 0}$

$\blue{\rm :\longmapsto\:y = 0}$

Substituting 'x = 1' in the given equation, we get

$\blue{\rm :\longmapsto\:y = 2 \times 1}$

$\blue{\rm :\longmapsto\:y = 2}$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 0 \\ \\ \sf 1 & \sf 2 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points

➢ See the attachment graph.

Consider,

$\green{\rm :\longmapsto\:y = 2x - \dfrac{1}{2}}$

Substituting 'x = 0' in the given equation, we get

$\green{\rm :\longmapsto\:y = 2 \times 0 - \dfrac{1}{2}}$

$\green{\rm :\longmapsto\:y = - \dfrac{1}{2}}$

$\green{\rm :\longmapsto\:y = - 0.5}$

Substituting 'x = 1' in the given equation, we get

$\green{\rm :\longmapsto\:y = 2 \times 1 - \dfrac{1}{2}}$

$\green{\rm :\longmapsto\:y = 2 - \dfrac{1}{2}}$

$\green{\rm :\longmapsto\:y = \dfrac{3}{2}}$

$\green{\rm :\longmapsto\:y = 1.5}$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf - 0.5 \\ \\ \sf 2 & \sf 1.5 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points

➢ See the attachment graph.

Now, From graph,

• we concluded that given lines are parallel.