1. Objective: To construct equations of straight lines from given graphs
Straight Line Graphs
Objective: To construct equations of straight lines from given graphs

2. Recap
What 4 facts can you say about the graph produced by the following equation?
y= 4x -2

3. y= 4x -2
It is linear
It has a positive gradient
The gradient is 4
It crosses the y-axes at -2

4. y= 4x -2
It crosses at
y= -2

5. Equation of a straight line
Y=mx+c
This is the general equation of a straight line.
What do you think the m and the c stand for?

6. The c tells us where it crosses the y axis.
Y=mx+c
The c tells us where it crosses the y axis.
The m stands for the gradient
Learn this!!!!

7. A. What are the y intercepts and the gradients of the following lines?
1) y= -2x ) y= 5x + 5
3) y= -6x ) y= -2x -4
5) y=x 6) y= -6x -10
B. 2 of the lines are parallel to each other and 2 cross at the same points on the y-axis. Name the pairs.

8. Example: Find the gradient and y-intercept of the line 3y=6x+2
Harder ones!
To answer the following you need to first make sure that the equations are in the form y=mx+c
Example: Find the gradient and y-intercept of the line 3y=6x+2
We need to “get rid of” the 3 on the LHS. To do this divide both sides by 3

9. 3y=6x+2 Dividing both sides by 3 gives: y=2x+2/3
So the gradient is 2 and it crosses the y-axis at 2/3
Question: What is the co-ordinate of the y-intercept?
ANSWER: (0, 2/3)

10. Now try these… Find the gradient of each line and the coordinate of the y-intercept
1) 2y= 4x ) 5y= 4x
3) 8y= 2x ) 2y+3=5x
5) 2x+y= ) x-4y=8
7) 3y +5= ) 6y -x = 3
9) 5y -2 =10x 10) 5y+4= 20x

11. Section 2: Finding the equation given the line
Plot the following points to get a straight line graph X y

12. You should get a graph that looks like this...

13. Pick points on the line for which the coordinates are easy to read (ie whole numbers)
Mark them with a cross

14. Now join the 2 points forming a right angled triangle

15. 15 5
Work out the distances parallel to the y-axis and the x-axes and label them on your graph

16. The gradient is found by: the difference in the y 15 5
The gradient is found by:
the difference in the y
the difference in the x =3
=15/5

17. Good!!! It is positive so it’s gradient is +315 5
Is the gradient positive or negative?
Good!!! It is positive so it’s gradient is +3

18. So what is the equation of our line?
Well we now know that the gradient is 3.
What else did we need to know to get our equation?
Remember: y=mx +c

19. Y=mx+c The c tells us where it crosses the y axis.
The m stands for the gradient
We’ve got the gradient so all we need now is the y-intercept

20. It crosses the y-axis at +4
That’s easy…just look at your graph to find where it crosses the y- axis...
It crosses the y-axis at +4

21. The gradient is +3 and the y-intercept is +4, so put these facts
So what is our equation?
The gradient is +3 and the
y-intercept is +4, so put these facts
into the general formula y=mx+c
Answer: y= 3x + 4

22. Then just put these values into y=mx+c …in the right place!!!
So remember:
To find the equation of a straight line, you need to work out the gradient (the triangle bit!!!) and the point where the line crosses the y-axis.
Then just put these values into y=mx+c …in the right place!!!

23. Now try this one… Find the equation of the line given by the following points: x y
ANSWER is y= 2x -4