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

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

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

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

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?

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!!!!

A. What are the y intercepts and the gradients of the following lines? 1) y= -2x +4 2) y= 5x + 5 3) y= -6x +4 4) 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.

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

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)

Now try these… Find the gradient of each line and the coordinate of the y-intercept 1) 2y= 4x - 10 2) 5y= 4x 3) 8y= 2x - 16 4) 2y+3=5x 5) 2x+y= 4 6) x-4y=8 7) 3y +5= 6 8) 6y -x = 3 9) 5y -2 =10x 10) 5y+4= 20x

Section 2: Finding the equation given the line Plot the following points to get a straight line graph X -3 -2 -1 0 1 2 3 4 y -5 -2 1 4 7 10 13 16

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

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

Now join the 2 points forming a right angled triangle

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

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

Good!!! It is positive so it’s gradient is +3 15 5 Is the gradient positive or negative? Good!!! It is positive so it’s gradient is +3

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

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

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

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

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!!!

Now try this one… Find the equation of the line given by the following points: x -3 -2 -1 0 1 2 3 y -10 -8 -6 -4 -2 0 2 ANSWER is y= 2x -4