Question

Draw the graph of a line y = 2x + 6 and y = x+3​

Answer 1

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

• Consider the line y = 2x + 6

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

$\rm :\longmapsto\:y = 2 \times 0 + 6$

$\rm :\longmapsto\:y =0 + 6$

$\bf\implies \:y = 6$

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

$\rm :\longmapsto\:y = 2 \times 1 + 6$

$\rm :\longmapsto\:y = 2 + 6$

$\bf\implies \:y = 8$

3. Substituting 'x = - 3' in the given equation, we get

$\rm :\longmapsto\:y = 2 \times ( - 3) + 6$

$\rm :\longmapsto\:y = - 6 + 6$

$\bf\implies \:y = 0$

Hᴇɴᴄᴇ,

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

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 6 \\ \\ \sf 1 & \sf 8 \\ \\ \sf - 3 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw graph using the points (0 , 6), (1 , 8) & (-3 , 0)

➢ See the attachment graph.

Now,

• Consider the second line y = x + 3

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

$\rm :\longmapsto\:y = 0 + 3$

$\bf\implies \:y = 3$

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

$\rm :\longmapsto\:y = 1+ 3$

$\bf\implies \:y = 4$

3. Substituting 'x = - 3' in the given equation, we get

$\rm :\longmapsto\:y = - 3 + 3$

$\bf\implies \:y = 0$

Hᴇɴᴄᴇ,

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

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 3 \\ \\ \sf 1 & \sf 4 \\ \\ \sf - 3 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw graph using the points (0 , 3), (1 , 4) & (-3 , 0)

➢ See the attachment graph.