Question

(i) Draw the graph (straight line) given by equation x − 3y = 18.

(ii) If the straight line drawn passes through the points (m,−5) and (6,n); find the values of m and n.

(iii) Also find the area of the triangle formed by the graph of line and both the axis.

Answer 1

(i) According to the question,

$x-3y=18\Rightarrow -3y=18-x\Rightarrow 3y=x-18$

The table for x-3y=18 is

x	9	0	6	3
y	-3	-6	-4	-5

(ii) Hence, from the graph, we can conclude that m=3 and n=-4.

(iii) If x = 0 then y = -6

Hence the line intersects the y axis at (0, -6)

If y = 0 then x = 18

Hence the line intersects the x – axis at (18, 0)

So the area of the triangle $=\frac{1}{2}\times 18\times 6=54uni{t}^2$