# Unit 14 Section 2 : Plotting Points on Straight Lines

In this section we will be plotting points that lie on a straight line.

We will then look for relationships between the x and y coordinates of the points on the line.

## Example

Below is a graph showing the points ( 1 , 3 ) , ( 2 , 4 ) , ( 3 , 5 ) , ( 4 , 6 ) , ( 5 , 7 )

We can then draw a straight line through all of the points: Note how the line goes all the way across the graph, not just between the points.

Equation of a line
We can find an equation which describes the relationship between the x and y coordinates on the graph.
Looking at the pairs of coordinates, we can see that the y-value is always two more than the x-value.

The equation to represent this is:
 y = x + 2 (the y-coordinate can always be found by adding 2 to the x-coordinate)
Note that this works for every point on the line, even with negative numbers and decimals.
Examples of other points on this line are: ( 0 , 2 ) , ( –1 , 1 ) , ( –4 , –2 ) and ( 2.5 , 4.5 )

## Practice Question

 Work out the answer to the question then click on the button marked to see whether you are correct. The points ( –1 , –3 ) , ( 0 , 0 ) , ( 1 , 3 ) and ( 2 , 6 ) have been plotted. A straight line has been drawn through the four points. How are the x and y coordinates of the points on the line related? What is the equation of the line?

## Exercises

Work out the answers to the questions below and fill in the boxes. Click on the button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on to see the answer.

 NOTE: In these questions you need to plot points and draw lines on graphs. To plot a point, just click on the graph with your left mouse button. To draw a line, hold down the left mouse button at one point on the line and drag the pointer to another point on the line. When you let go of the button the line will appear and it will automatically cross the whole graph. If you make a mistake, press the delete key and the graph will be cleared.

Question 1
(a) Plot these points on the graph and draw a straight line through them:
( 0 , 4 ) , ( 1 , 5 ) , ( 3 , 7 ) , ( 4 , 8 )
(a) When you have finished, click

(b) Below are the coordinates of three other points on the line.
(b) Fill in the gaps:

 ( 2 , ) ( –2 , ) ( , 9 )

Question 2
 You need to upgrade your Flash PlayerGo to http://www.adobe.com/go/getflashplayer. (a) Plot these points on the graph and draw a straight line through them: ( 0 , 6 ) , ( 2 , 4 ) , ( 3 , 3 ) , ( 5 , 1 ) (a) Now plot these points on the graph and draw another line through them: ( 1 , 8 ) , ( 2 , 7 ) , ( 5 , 4 ) , ( 7 , 2 ) (a) When you have finished, click (b) These two lines are Parallel Perpendicular

Question 3
 You need to upgrade your Flash PlayerGo to http://www.adobe.com/go/getflashplayer. (a) Plot these points on the graph and draw a straight line through them: ( 2 , 6 ) , ( 3 , 5 ) , ( 4 , 4 ) , ( 7 , 1 ) (a) Now plot these points on the graph and draw another line through them: ( 0 , 1 ) , ( 1 , 2 ) , ( 3 , 4 ) , ( 5 , 6 ) (a) When you have finished, click (b) These two lines are Parallel Perpendicular

Question 4
(a) Plot these points on the graph and draw a straight line through them:
( 1 , 1 ) , ( 2 , 2 ) , ( 4 , 4 ) , ( 5 , 5 )
(a) When you have finished, click

(b) Below are the coordinates of two other points on the line.
(b) Fill in the gaps:

 ( 3 , ) ( , 7 )

(c) Complete the equation of the line:

y =

Question 5
(a) Plot these points on the graph and draw a straight line through them:
( 1 , 3 ) , ( 2 , 4 ) , ( 3 , 5 ) , ( 5 , 7 )
(a) When you have finished, click

(b) Below are the coordinates of three other points on the line.
(b) Fill in the gaps:

 ( 0 , ) ( –1 , ) ( , 8 )

(c) Complete the equation of the line:

y =

Question 6
(a) Plot these points on the graph and draw a straight line through them:
( 0 , 5 ) , ( 2 , 3 ) , ( 4 , 1 ) , ( 5 , 0 )
(a) When you have finished, click

(b) Below are the coordinates of two other points on the line.
(b) Fill in the gaps:

 ( 3 , ) ( , 4 )

(c) Complete the equation of the line:

x + y =

Question 7
 You need to upgrade your Flash PlayerGo to http://www.adobe.com/go/getflashplayer. (a) Plot these points on the graph and draw a straight line through them: ( –3 , –4 ) , ( –1 , –2 ) , ( 1 , 0 ) , ( 4 , 3 ) (a) When you have finished, click (b) Complete the equation of the line: y =

Question 8
 You need to upgrade your Flash PlayerGo to http://www.adobe.com/go/getflashplayer. (a) Plot these points on the graph and draw a straight line through them: ( –2 , –4 ) , ( 2 , 4 ) , ( 3 , 6 ) , ( 4 , 8 ) (a) When you have finished, click (b) Complete the equation of the line: y =

You have now completed Unit 14 Section 2
 Your overall score for this section is Correct Answers You answered questions correctly out of the questions in this section. Incorrect Answers There were questions where you used the Tell Me button. There were questions with wrong answers. There were questions you didn't attempt.
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