Straight Line Graphs

1
Straight Line Graphs
NC Level 7

• 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
Ymxc This is the general equation of a straight
line.
What do you think the m and the c stand for?
6
Ymxc
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 4 2) y 5x 5 3) y -6x 4
4) y -2x -4 5) yx 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
Harder ones!
To answer the following you need to first make
sure that the equations are in the form
ymxc Example Find the gradient and
y-intercept of the line 3y6x2
We need to get rid of the 3 on the LHS. To do
this divide both sides by 3
9
3y6x2
Dividing both sides by 3 gives y2x2/3 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 theseFind the gradient of each line and
the coordinate of the y-intercept
1) 2y 4x - 10 2) 5y 4x 3) 8y 2x - 16
4) 2y35x 5) 2xy 4 6) x-4y8 7) 3y 5
6 8) 6y -x 3 9) 5y -2 10x 10)
5y4 20x
11
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
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
15
5
The gradient is found by the difference in the y
the difference in the x
3
15/5
17
15
5
Is the gradient positive or negative?
Good!!! It is positive so its 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 ymx c
19
Ymxc
The c tells us where it crosses the y axis.
The m stands for the gradient
Weve got the gradient so all we need now is the
y-intercept
20
Thats easyjust look at your graph to find where
it crosses the y- axis...
It crosses the y-axis at 4
21
So what is our equation?
The gradient is 3 and the y-intercept is 4, so
put these facts into the general formula ymxc
Answer y 3x 4
22
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 ymxc
in the right place!!!
23
Now try this oneFind the equation of the
line given by the following pointsx -3 -2
-1 0 1 2 3 y -10 -8 -6 -4 -2
0 2
ANSWER is y 2x -4