Question

Express the equation x + ½ y – 3 = 0 as x in terms of y and hence check if point (5,-4) lies on the graph of the equation.

Answer 1

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

Given linear equation is

$\rm :\longmapsto\:x + \dfrac{1}{2}y - 3 = 0$

$\rm :\longmapsto\:x = 3 - \dfrac{1}{2}y$

So, is the required expression for x in terms of y.

Let we plot the graph of above equation.

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

$\rm :\longmapsto\:x = 3 - \dfrac{1}{2} \times 0$

$\rm :\longmapsto\:x = 3 - 0$

$\rm :\longmapsto\:x = 3$

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

$\rm :\longmapsto\:x = 3 - \dfrac{1}{2} \times 2$

$\rm :\longmapsto\:x = 3 - 1$

$\rm :\longmapsto\:x = 2$

Substituting 'y = 4' in the given equation, we get

$\rm :\longmapsto\:x = 3 - \dfrac{1}{2} \times 4$

$\rm :\longmapsto\:x = 3 - 2$

$\rm :\longmapsto\:x = 1$

Hᴇɴᴄᴇ,

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

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 3 & \sf 0 \\ \\ \sf 2 & \sf 2 \\ \\ \sf 1 & \sf 4 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (0 , 3), (2 , 2) & (4 , 1)

➢ See the attachment graph.

From graph, we concluded that point (5, - 4) lies on it.

Answer 2

Step-by-step explanation:

Solution−

Given linear equation is

:

⟼

x

+

1

2

y

−

3

=

0

:⟼x+

2

1

y−3=0

:

⟼

x

=

3

−

1

2

y

:⟼x=3−

2

1

y

So, is the required expression for x in terms of y.

Let we plot the graph of above equation.

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

:

⟼

x

=

3

−

1

2

×

0

:⟼x=3−

2

1

×0

:

⟼

x

=

3

−

0

:⟼x=3−0

:

⟼

x

=

3

:⟼x=3

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

:

⟼

x

=

3

−

1

2

×

2

:⟼x=3−

2

1

×2

:

⟼

x

=

3

−

1

:⟼x=3−1

:

⟼

x

=

2

:⟼x=2

Substituting 'y = 4' in the given equation, we get

:

⟼

x

=

3

−

1

2

×

4

:⟼x=3−

2

1

×4

:

⟼

x

=

3

−

2

:⟼x=3−2

:

⟼

x

=

1

:⟼x=1

Hᴇɴᴄᴇ,

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

➢ Now draw a graph using the points (0 , 3), (2 , 2) & (4 , 1)

➢ See the attachment graph.

From graph, we concluded that point (5, - 4) lies on it