Question

Draw the graph of the equation 2x+y =7. From the graph :
a) Find whether the point (3,4) lies on the graph.
b) Find whether x=3 , y=1 is a solution of the equation .
c) Find the value of x , when y=1 .
d) Find the point where the equation meets the x-axis .

Answer 1

Answer is attached guys

Answer 2

The graph of equation $\bf2x + y = 7$ is attached.

a) Point (3,4) does not lies on the line.

b) The point (3,1) is a solution of equation.

c) The value of x is 3.

d) The point is C(3.5,0), where line meets at x-axis.

Step by step Explanation:

Given:

• An equation.
• $2x + y= 7$

To find:

a) Find whether the point (3,4) lies on the graph.

b) Find whether x=3 , y=1 is a solution of the equation .

c) Find the value of x , when y=1 .

d) Find the point where the equation meets the x-axis .

Solution:

Concept to be used:

• Find at least two points/solution of the equation.
• Plot the points on the graph.
• Draw the line while joining these points.

Step 1:

Draw the line.

put x=0 in the equation.

$2(0) + y = 7$

or

$y = 7$

Let it is point D(0,7).

Put y=0.

$2x + 0 = 7$

or

$2x = 7$

or

$x = 3.5$

Let the point is C(3.5,0).

Mark the points on the graph and draw the line.

*see the attachment.

Step 2:

a) Find the position of the point (3,4).

Mark the point A(3,4) on the graph.

It is clear that point (3,4) does not lies on the line.

Step 3:

b) Find whether x=3 , y=1 is a solution of the equation.

Put x=3 and y=1 in the equation.

$2(3) + 1 = 7$

or

$6 + 1 = 7$

or

$7 = 7$

The point B(3,1) is a solution of equation.

The point lies on the line.

*see the attachment.

Step 4:

c) Find the value of x, when y=1.

Put y= 1 in the equation.

$2x + 1 = 7$

or

$2x = 6$

or

$x = 3$

Thus,

The value of x is 3.

Step 5:

d) Find the point where the equation meets the x-axis.

The point is C(3.5,0), where line meets at x-axis.

Thus,

a) Point (3,4) does not lies on the line.

b) The point (3,1) is a solution of equation.

c) The value of x is 3.

d) The point is C(3.5,0), where line meets at x-axis.

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