1. ©G Dear2008 – Not to be sold/Free to use
Stage 4
Year 9
Coordinate
Geometry
Equation of a
Straight Line
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©G Dear2008 – Not to be sold/Free to use

2. We must be able to convert between forms.
Equation of a Straight Line
Two types of equation.
1. Gradient-Intercept Form
y = mx +b
Gradient
y-Intercept
2. General Form
ax +by + c = 0
‘a’ always positive.
‘b’ NOT
y-intercept
Always ‘0’
We must be able to convert between forms.

3. Equation of a Straight Line
Write in General Form
a) y = 2x + 3
b) 2y = x +7 -y -y
-2y
-2y
0 = 2x – y + 3
0 = x – 2y +7
2x –y +3 = 0
x – 2y +7 = 0 x 3 x3
c) y = -x + 6
d) y = +3 x3
+x -6
+x -6 x3
x + y - 6 = 0
3y = x + 9
-3y
-3y
0 = x -3y + 9
x -3y + 9 = 0

4. Equation of a Straight Line
Write in Gradient-Intercept Form
a) 3y = 9x + 6
b) 5y = 2x + 1 ÷3 ÷3 ÷3 ÷5 ÷5 ÷5
y = 3x + 2 2 5 1 5
y = x +
c) y - 2x = 0
d) 3y + x -1 = 0
+2x
+2x -x +1 -x +1
y = 2x
3y = -x +1 ÷3 ÷3 ÷3 -1 3 1 3
y = x +

5. Equation of a Straight Line
Write the Gradient and Y-Intercept 1 2
a) y = 9x + 6
b) y = x - 1 1 2
m = 9
m =
b = 6
b = -1
c) y = 2x
d) y = x + 7
m = 2
m = 1
b = 0
b = 7

6. Equation of a Straight Line
Write the equation. y = mx + b 2 3
a) m=2 b=1
b) m= b=-5
y = 2x + 1 2 3
y = x - 5
c) m= b=-1
d) m=12 b=7
y = -4x - 1
y = 12x + 7

7. Write the equation as y=mx+b and state m and b.
Equation of a Straight Line
Write the equation as y=mx+b and state m and b.
a) y – 2x = 1
b) 2y = 3x + 7
+2x
+2x ÷2 ÷2 ÷2
y = 2x + 1 3 2 7 2
y = x +
m = 2 3 2
m =
b = 1 7 2
b =

8. Is the point given on the line?
Equation of a Straight Line
Is the point given on the line?
a) y = 2x + 1 (2,5)
b) 2y = 3x + 7 (1,4)
5 = 2x2 + 1
2x4 = 3x1 + 7
5 = 5
Yes
8 = 10 No
c) y – 2x = 1 (1,3)
d) y = 5x + 1 (1,5)
3 - 2x1 = 1
5 = 5x1 + 1
1 = 1
Yes
5 = 6 No