Question

Make graph for the question in attachment, also give step by step explaination.​

Answer 1

Given Question :-

Draw the graph of the equation x/5 + y/6 = 1. Also, find the area of the triangle formed by the line and the coordinate axis.

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

Given equation of line is

$\rm :\longmapsto\:\dfrac{x}{5} + \dfrac{y}{6} = 1$

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

$\rm :\longmapsto\:\dfrac{0}{5} + \dfrac{y}{6} = 1$

$\rm :\longmapsto\:0 + \dfrac{y}{6} = 1$

$\rm :\longmapsto\:\dfrac{y}{6} = 1$

$\bf\implies \:y = 6$

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

$\rm :\longmapsto\:\dfrac{x}{5} + \dfrac{0}{6} = 1$

$\rm :\longmapsto\:\dfrac{x}{5} + 0 = 1$

$\rm :\longmapsto\:\dfrac{x}{5} = 1$

$\bf\implies \:x = 5$

Hᴇɴᴄᴇ,

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

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 6 \\ \\ \sf 5 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (0 , 6) & (5 , 0)

➢ See the attachment graph.

Now, Required triangle is OAB and such that

➢ OA = 5 units

➢ OB = 6 units

So,

$\rm\implies \:Area_{(\triangle OAB)}$

$\rm \:  =  \: \dfrac{1}{2} \times OA \times OB$

$\rm \:  =  \: \dfrac{1}{2} \times 5 \times 6$

$\rm \:  =  \: 15 \: square \: units$

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Remark :-

The area of triangle formed by the line ax + by + c = 0 with the coordinates axis is given by

$\rm\implies \: \boxed{\tt{ \: Area_{(\triangle )} = \dfrac{ {c}^{2} }{ |2ab| } \: }}$