Question

please answer this question

Find some ordered (x ,y) such that x +2y = 5 and plot them . What do you get when you join these points? How many such ordered pairs can be found and plotted?​

Answer 1

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

The given equation is

$\rm :\longmapsto\:x + 2y = 5$

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

$\rm :\longmapsto\:0 + 2y = 5$

$\rm :\longmapsto\:2y = 5$

$\rm :\longmapsto\:y = 2.5$

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

$\rm :\longmapsto\:x + 2(0) = 5$

$\rm :\longmapsto\:x + 0 = 5$

$\rm :\longmapsto\:x = 5$

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

$\rm :\longmapsto\:x + 2(1) = 5$

$\rm :\longmapsto\:x + 2= 5$

$\rm :\longmapsto\:x = 5 - 2$

$\rm :\longmapsto\:x = 3$

Substituting 'y = 2' in the given equation, we get

$\rm :\longmapsto\:x + 2(2) = 5$

$\rm :\longmapsto\:x + 4 = 5$

$\rm :\longmapsto\:x = 5 - 4$

$\rm :\longmapsto\:x = 1$

Hᴇɴᴄᴇ,

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

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 2.5 \\ \\ \sf 5 & \sf 0 \\ \\ \sf 3 & \sf 1\\ \\ \sf 1 & \sf 2 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points.

➢ See the attachment graph.

From graph, we conclude that

1. When we join these points, we get a line

2. Infinitely many ordered pair exist.