Graphs

In a graph the horizontal line is x-axis and the vertical line is y-axis, and the point of intersection of x and y-axis is the origin (0,0).

So, at any point the first number if x-coordinate and the second number is y-coordinate.

For A (4,0) move 4 unit in the x-direction and 0 unit in the y-direction, means the point A is on the x-axis.

For B (0,6) move 0 unit in the x-direction and 6 unit in the y-direction, means the point B is on the y-axis.

For C (2,5) move 2 unit in the x-direction and 5 unit in the y-direction.

For D (7,1) move 7 unit in the x-direction and 1 unit in the y-direction.

For E ([], 5) move 5 unit in the y-direction, so this will be a point on the line y=5, i.e., parallel to the x-axis. So let it be E(1,5).

Similarly, for E ([], 5) move 5 unit in the y-direction, so this point will also be on the line y=5, i.e., parallel to the x-axis. So let it be F(5,5)

So the graph of the given points is as shown below.

In a graph the horizontal line is x-axis, and the vertical line is y-axis, and the point of intersection of x and y-axis is the origin (0,0).

So at any point the first number if x-coordinate and the second number is y-coordinate.

For (1, 1) move 1 unit in x-direction and 1 unit in y-direction.

For (3,7) move 3 unit in x-direction and 7 unit in y-direction.

For (9,1) move 9 unit in x-direction and 1 unit in y-direction.

For (12,1) move 12 unit in x-direction and 1 unit in y-direction.

So the graph of the given points is as shown below.

From the above graph we can see that point (1,1), (9,1) and (12,1) lie on a single line.

Let’s take points points (0,2), (1,3), (2,4) and (5,5)

For (0,2) move 2 unit in the y-direction, this point will be on the y-axis.

For (1,3) move 1 unit in the x-direction and 3 unit in the y-direction.

For (2,4) move 2 unit in the x-direction and 4 unit in the y-direction.

For (5, 7) move 5 units in the x-direction and 7 units in the y-direction.

By putting three more collinear points on the graph will be as shown in the below figure

So the points A(0,2), B(1,3), C(2,4) and D(4, 6) are on the same line, so they are collinear points.

Plotting the points on the graph sheet from the coordinates of the points and joining the points, we will get a picture which is called as graph.

If we get straight line after joining points, then such type of graph is known as Linear graph.

Let 1 exercise book= length of 5 sides of the smallest squares along x-axis, i.e., x-axis represents the Number of an exercise book.

And 10 rs = length of 5 sides of the smallest square along y-axis, i.e., y-axis represent the price of the exercise book.

The given data are collinear, i.e., meet on a single line; we will call it a linear line.

(i) We will find out the price of 6 exercise books

From the graph we can see that drawing a line from 6 on the x-axis to the linear line, we will mark this point it is (6,30).

So the price of the 6 exercise books is Rs. 30.

(ii) We will find the number of exercise books for Rs. 45

From the graph we can see that drawing a line from 45 on the y-axis to the linear line, we will mark this point it is (9,45).

So the number of exercise books for Rs. 45 is 9.

Let 1 hour = length of 5 sides of the smallest squares along x-axis, i.e., x-axis represents the Time (in hours).

And 25 km = length of 5 sides of the smallest square along y-axis, i.e., y-axis represent the distance (in km).

The given data are collinear, i.e., meet on a single line; we will call it a linear line.

(i) We will find the distance covered in 4 hrs

From the graph we can see that drawing a line from 4 on the x-axis to the linear line, we will mark this point it is (4,100).

So the distance covered in 4 hrs is 100 km.

(ii) We will find how long it will take to cover 150 km

From the graph we can see that drawing a line from 150 on the y-axis to the linear line, we will mark this point it is (6,150).

So the time taken to cover 150km is 4 hours.

(i) The coordinates of any point can be found by counting the number of units from the origin (0). First we find the x-coordinate of the point by counting the points distance on x-axis and similarly we find the y-coordinate of the point by counting the points distance on y-axis.

So the coordinates of the given points are as shown in the below figure.

(ii) If the three or more points lie on same line these points are collinear in nature.

So from above figure we see that points F, G and H are collinear

Points I, J and K are collinear

Points C, D and E are collinear

(iii) If the points doesn’t lie on same line these points are not collinear in nature.

So from above figure we see that points A, F, I, C are not collinear

In a graph the horizontal line is x-axis and the vertical line is y-axis, and the point of intersection of x and y axis is the origin (0,0).

So in any point the first number if x-coordinate and the second number is y-coordinate.

So the graph of the given points is as shown below.

(i) The plot of the given points is as shown in below graph:

For (1,1) move 1 unit in x direction and 1 unit in y direction.

For (2,2) move 2 unit in x direction and 2 unit in y direction.

For (3,3) move 3 unit in x direction and 3 unit in y direction.

From the graph it can be seen that the three points are on same line hence they are collinear in nature.

(ii) Let’s take three points (1,4), (2,4) and (1,3).

For (1,4) move 1 unit in x direction and 4 unit in y direction.

For (2,4) move 2 unit in x direction and 4 unit in y direction.

For (1,3) move 1 unit in x direction and 3 unit in y direction.

By putting three non collinear points on the graph will be as shown in below figure

So from graph it can be seen that the three points D, E and F are not on same line, and hence are non collinear points in nature.

(iii) Let’s take three points (0,2), (1,3) and (2,4).

For (0,2) move 2 unit in y direction, this point will be on y-axis.

For (1,3) move 1 unit in x direction and 3 unit in y direction.

For (2,4) move 2 unit in x direction and 4 unit in y direction.

By putting three more collinear points on the graph will be as shown in below figure

So the points D(0,2), E(1,3) and F(2,4) are on same line so they are collinear points other than the given points.

(i) From the given condition for x and y axis, and observing from the graph it can be seen that the one guava cost 3 rupees. And the graph shows the sale of 10 guavas.

(ii) As one guava cost 3 rupees hence 4 guavas cost 4×3=12 rupees. And from the graph it can be seen that (4, 12) is one of the point on the line, so the x coordinate represents the number of guavas and y coordinates represents the cost of those guavas.

(iii) From the graph it can be seen that for Rs. 30 we get 10 guavas as (10, 30) is a point on the line. And from relation, as one guava cost 3 rupees hence 4 guavas cost 10×3=30 rupees.

(iv) From the graph it can be seen that for Rs. 9 we get 3 guavas as (3, 9) is a point on the line. And from relation, as one guava cost 3 rupees hence 4 guavas cost 3×3=9 rupees.

(v) As one guava cost 3 rupees hence 9 guavas cost 9×3=27 rupees. And from the graph it can be seen that (9, 27) is a point on the line, so the x coordinate represents the number of guavas and y coordinates represents the cost of those guavas.

(i) From the given condition for x and y axis, and observing from the graph it can be seen that for one hour the distance covered is 30km.

The relation is linear for the time and distance. As time increases the distance covered also increases.

(ii) As in 1 hour, 30 km distance is covered hence 3 hours the distance covered is 3×30=90 km. And from the graph it can be seen that (3, 90) is one of the point on the line, so the x coordinate represents the time in hours and y coordinates represents the distance in km.

(iii) As in 1 hour, 30 km distance is covered hence for 120km the time taken is hours. And from the graph it can be seen that (4, 120) is one of the point on the line, so the x coordinate represents the time in hours and y coordinates represents the distance in km. the time required to cover 120 km.

(iv) The formula for velocity is, hence the velocity will be km per hour. Hence for 1 hour distance covered is 30 km, so the corresponding velocity will 30 km/hr And for 2 hour distance covered is 60 km, so the corresponding velocity will 30 km/hr. So the graph has velocity of 30km/hr.

(v) As in 1 hour, 30 km distance is covered hence hours the distance covered is km. And from the graph it can be seen that (2.5, 75) is one of the point on the line, so the x coordinate represents the time in hours and y coordinates represents the distance in km

(vi) As in 1 hour, 30 km distance is covered hence for 45km the time taken is hours. And from the graph it can be seen that (1.5, 45) is one of the point on the line, so the x coordinate represents the time in hours and y coordinates represents the distance in km. the time required to cover 45 km.

Let 1 pencil=length of a side of the smallest squares along x-axis, i.e., x-axis represents the number of pencil.

And 1 rupee = length of a side of the smallest square along y-axis i.e., y-axis represent the price of the pencil

The points of the graph can be represented as shown above. They lie on a line.

A graph in which we obtain a line on joining all the points is called a liner graph. Hence the graph obtained from the data given is a liner graph.

Let 2 hour=length of 5 sides of the smallest squares along x-axis i.e., x-axis represents the time in hours.

And 20km = length of 5 sides of the smallest square along y-axis i.e., y-axis represent the distance in km.

The points of the graph can be represented as shown above. They lie on a line.

A graph in which we obtain a line on joining all the points is called a liner graph. Hence the graph obtained from the data given is a liner graph.

Let 1 bag=length of 1 side of the smallest squares along x-axis i.e., x-axis represents the number of bags.

And 10 unit = length of 1 sides of the smallest square along y-axis i.e., y-axis represent the price of the bags.

The points of the graph can be represented as shown above. They lie on a line.

A graph in which we obtain a line on joining all the points is called a liner graph. Hence the graph obtained from the data given is a liner graph.

Let 1 book=length of 5 sides of the smallest squares along x-axis i.e., x-axis represents the number of books.

And 20 unit = length of 5 sides of the smallest square along y-axis i.e., y-axis represent the price of the books.

The points of the graph can be represented as shown above. They lie on a line.

A graph in which we obtain a line on joining all the points is called a liner graph. Hence the graph obtained from the data given is a liner graph.

Let 1 over=length of 1 side of the smallest squares along x-axis i.e., x-axis represents the number of over.

And 1 run= length of 5 side of the smallest square along y-axis i.e., y-axis represent the scores at the end of the over.

The points of the graph can be represented as shown above. They lie on a line.

A graph in which we obtain a line on joining all the points is called a liner graph. Hence the graph obtained from the data given is a liner graph.