Question

Draw a graph of the equation 2x + 3y + 5 = 0, from the graph find the value of:
(i) x, when y = -3
(ii) y, when x = 8

Answer 1

We have
2x + 3y + 5 = 0
⇒ 2x + 3y = -5
⇒ 3y = -5 - 2x

⇒ y = ${\displaystyle \frac{-2x-5}{3}}$
When x = -2

⇒ y = ${\displaystyle -\frac{1}{3}}$ = 0.33
When x = 0

⇒ y = ${\displaystyle -\frac{5}{3}}$ = -1.66
When x = 2

⇒ y = ${\displaystyle -\frac{9}{3}}$ = -3

x	-2	-1	0	1	2
y	-0.33	-1	-1.66	-2.33	-3

Thus ordered pairs of 2x + 3y + 5 = 0 are {{-2, -0.33), (-1, -1), (0, -1.66), (1, -2.33),(2, -3)}. Hence graph is a below.

(i) x, when y = -3
From graph we find that x = 2, when y = -3
(ii) y, when x = 8
From graph we find that y = -7, when x = 8.