Question

Draw the graph of x+y=4. Name the vertices of triangle formed between this line and coordinate axis (both x & y axis)​

Answer 1

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

Given equation of line is

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

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

$\rm :\longmapsto\:0 + y = 4$

$\rm \implies\:\boxed{ \tt{ \: y = 4 \: }}$

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

$\rm :\longmapsto\:x + 0 = 4$

$\rm \implies\:\boxed{ \tt{ \: x = 4 \: }}$

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

$\rm :\longmapsto\:2 + y = 4$

$\rm :\longmapsto\:y = 4 - 2$

$\rm \implies\:\boxed{ \tt{ \: y = 2 \: \: }}$

Hᴇɴᴄᴇ,

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

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 4 \\ \\ \sf 2 & \sf 2 \\ \\ \sf 4 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (0 , 4), (2 , 2) & (4 , 0)

➢ See the attachment graph.

From graph, we conclude that required triangle is ABC.

Coordinates of A ( 4, 0 )

Coordinates of B ( 2, 2 )

Coordinates of C ( 0, 4 )