Question

Draw the graph of each of the equations given below. Also, find the coordinates of the points where the graph cuts the coordinate axes:
(i) 6x–3y=12
(ii) -x+4y=8
(iii) 2x+y=6
(iv) 3x+2y+6=0

Answer 1

1. $(0,-4)$

2. $(0,2)$

3. $(0,6)$

4. $(0,-3)$

Step-by-step explanation:

$(i)6x-3y=12$

put $x=0$

$6\times0-3y=12\\0-3y=12\\-3y=12\\y=\frac{12}{-3}\\y=-4$

put $y=-4$ in equation(i)

$6x-3y=12\\6x-3(-4)=12\\6x=0\\x=\frac{0}{6}\\x=0\\=(0,-4)$

$(ii)-x+4y=8$

put $x=0$

$0+4y=8\\4y=8\\y=2$

put $y=2$ in equation (i)

$-x+4\times2=8\\-x+8=8\\-x=8-8\\-x=0\\(0,2)$

$(iii)2x+y=6$

put $x=0$

$2\times0+y=6\\0+y=6\\y=6$

put $y=6$ in equation (i)

$2x+y=6\\2x+6=6\\2x=0\\x=0\\(0,6)$

$(iv)3x+2y=-6$

put $x=0$

$2y=-6\\y=-3$

put $y=-3$ in equation (i)

$3x+2(-3)=-6\\3x-6=-6\\3x=0\\x=0\\=(0,-3)$

Answer 2

Coordinates and graph are as follows:

• 6x–3y=12

for x=0 y=-4

for x=2 y=0

• Required coordinates (0,-4)&(2,0)

• -x+4y=8

for x=0 y=2

for x=-8 y=0

• Required coordinates (0,2)&(-8,0)

•2x+y=6

for x=0 y=6

for x=3 y=0

• Required coordinates (0,6)&(3,0)

•3x+2y+6=0

for x=0 y=-3

for x=-2 y=0

• Required coordinates (0,-3)&(-2,0)