Question

1. Draw the graphs of linear equations
y = x and y=-x on the same cartesian plane.
What do you observe?
2. Determine the point on the graph of the linear equation 2x + 5y = 19, whose
ordinate is 1- times its abscissa.
3. Draw the graph of the equation represented by a straight line which is parallel to
the x-axis and at a distance 3 units below it.
4. Draw the graph of the linear equation whose solutions are represented by the
points having the sum of the coordinates as 10 units.
5. Write the linear equation such that each point on its graph has an ordinate 3 times
its abscissa​

Answer 1

Answer:

Step-by-step explanation:

Problem 1:

Given:

Draw the graphs of linear equations

y = x and y=-x on the same cartesian plane.

What do you observe?

Solution:

Equation : y = x

Keeping x = 1 , 2 and 3 once

y = 1 , y = 2 and y = 3.

Coordinates are : ( 1, 1 );( 2, 2 );( 3, 3 )

Equation, y = - x

Keeping y = 1 , 2 and 3

1 = - x , 2 = - x and 3 = - x

Coordinates are : ( - 1, 1 );( - 2, 2 );( - 3, 3 )

On plotting both equations we get,

That two equation intersect at coordinate (0,0) i.e. origin.

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Problem 2:

Given:

Determine the point on the graph of the linear equation 2x + 5y = 19, whose  ordinate is 1- times its abscissa.

Solution:

Let the abscissa be x.

Then the ordinate = 3/2a .

Now, Coordinates of the point ( a, 3/2a ) .

Also, Given that it is a point on the line 2x + 5y = 19

Now,

2(a) + 5(3/2a) = 19

2a + 15/2a = 19

19a = 38

a = 2 .

Now, Abscissa = 2 .

Ordinate = 3/2(2)= 3 .

(The required point is 2,3)

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Problem 3:

Given:

Draw the graph of the equation represented by a straight line which is parallel to  the x-axis and at a distance 3 units below it.

Solution:

Please find the attached diagram.

We know,

The equation of line parallel to the x- axis, y=a

And a is distance with respect to x- axis.

So, a= -3  

Therefore, the equation of straight line, y= -3

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Problem 4:

Given:

Draw the graph of the linear equation whose solutions are represented by the  points having the sum of the coordinates as 10 units.

Solution:

According to the question,

x + y = 12,

The graph is attached as the pic

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Problem 5:

Given:

Write the linear equation such that each point on its graph has an ordinate 3 times  its abscissa​?

Solution:

Solution :

Required linear equation  

y = 3x

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