1. Gradient-Intercept method (Used when the graph passes through (0;0))
GRADE 9 GRAPHS
Std form: y = mx + c
1. THE STRAIGHT LINE GRAPH:
gradient
y-intercept
How to Draw a Straight Line Graph:
Intercept-Intercept Method (Used if there is an x-term, a y-term and a number)
Gradient-Intercept method (Used when the graph passes through (0;0))
i.e when x = 0, y = 0).
Special Lines:
y = c
x = k
y = x
y = -x

2. Always show the x and y intercepts.
Intercept-Intercept Method (Used if there is an x-term, a y-term and a number)
Step 1:
y-int
Let x = 0
NOTE: Equation does not have to be in std form.
Always show the x and y intercepts.
Step 2:
x-int
Let y = 0
Step 3:
Join the 2 intercepts.
Eg: On the same axes, draw rough graphs of: 2x + 4y = 8 and 2x – y = 3 y
2x + 4y = 8:
2x + 4y = 8
2x – y = 3 2
y-int:
if x = 0,
0 + 4y = 8
... y = 2
4y = 8 x 4 __ _ 1½ 4 -3
x-int:
if y = 0
2x + 0 = 8
... 2x = 8 2 2
... x = 4
2x – y = 3
y-int:
if x = 0,
0 - y = 3
... y = -3
x-int:
if y = 0
2x - 0 = 3
... x = 3/2

3. *** *** Gradient-Intercept Method:
Use this when the graph passes through (0;0)
– will have an x-term, y-term and no other number other than 0.
NOTE: - The equation MUST be in standard form
-You will know to use this method – when x = 0, you get y = 0.
***
Always show the gradient
Step 1:
Get equation into std form
Step 2:
mark c = ..
Step 3:
Apply gradient m = … and move from c
Eg: On the same set of axes, draw rough graphs of x – 2y = 0 and y = -2x y
x – 2y = 0
y = ½x
Y-int,
x=0.
So 0 – 2y = 0
So – 2y = 0 2 1 x
***
So y = 0
Step 1:
std form
-2y = -x
SO -2y = -x
y = ½x
Step 2:
c = 0 1
m = --- 2
Step 3:

4. *** *** Step 1: Get equation into std form Step 2: mark c = .. Step 3:
Apply gradient m = … and move from c
Eg: On the same set of axes, draw rough graphs of x – 2y = 0 and y = -2x y
x – 2y = 0
y = ½x
Y-int, x=0.
So 0 – 2y = 0
So – 2y = 0 2 1 x
***
So y = 0 2
Step 1:
std form
-2y = -x
SO -2y = -x
y = ½x 1
y = – 2x
Step 2:
c = 0
y = – 2x 1
m = --- 2
y-int, x=0.
So y = 0
Step 3:
***
Step 1:
std form
y = – 2x
Step 2:
c = 0 2
Step 3:
m = -
--- 1

5. Special Lines:
Horizontal and Vertical Graphs:
y = c
and x = k
y = c cuts y-axis at c. NB: m = 0
x = k cuts x-axis at k. NB: m is infinitely large
Eg: On the same set of axes, draw rough graphs of y = 2 and x = -3.
y = c e.g. y = 2 y
x=-3
y = 2 no matter what x is.
y is always 2.
NB: mark 2 on y-axis,
and show parallel to x-axis
y=2 2
x = k e.g. x = - 3 -3 x
x = - 3 no matter what y is.
X is always -3.
NB: mark – 3 on x-axis
and show parallel to y-axis

6. Graphs of y = x and y = -x. y
y = x
y = -x 1
y = x 1
If x = 0,
y=0
If x = 0,
y=0 x
 grad-int 1
grad-int 1
c = 0
y = – x
c = 0
m = = so
m = = so
45° 1
NOTE:
45° 1

7. x
- 3 1 2 4 d y c a b
Finding the Equation of a Straight Line
STEPS:
i write y = mx + c
ii c =
iii m =
iv Subst into y = mx + c
Worked examples:
Find the equations of a, b, c and d
(Use steps i-iv except for types like c and d) a:
step 1:
y = mx + c b:
step 1:
y = mx + c c:
y = 2 no matter what x is.
step 2:
c = 2
step 2:
c = 2
y is always 2. 2
step 3:
m = + --
step 3:
m = - --
y = 2 3 1
y =
x + 2 d:
x = 4 no matter what y is.
step 4:
step 4:
y = - 2x
x is always 4.
x = 4

8. 3. Find the point of intersection of the lines
a) y1 = 2x and y2 = - x + 3
They cut where they are equal
y1 = y2
Subst for x in y = 2x
 y = 2(1) = 2
 2x = - x + 3
(1 ; 2)
2x + x = 3
 3x = 3
 x = 1
b) y1 = - 2x and y2 = - x + 3
They cut where they are equal
y1 = y2
Subst for x in y = -2x
 y = - 2(-3) = 6
- 2x = - x + 3
(-3 ; 6)
-2x + x = 3
 -x = 3
 x = -3
© Dr Linda & David Emery 2009