The document discusses the standard equation of a straight line, y = mx + c, where m is the gradient and c is the y-intercept. It provides examples of finding the equation of a line given m and the y-intercept, or two points on the line. The document also discusses finding the angle a line makes with the x-axis given its gradient, and the special cases of horizontal and vertical lines where the equation is either y = b or x = a, respectively.

1. Block 1
y = mx + c

2. What is to be learned?
• How to use the standard equation of a
straight line.

3. Is in form
y = mx + c
Ex 1 y = - ¾ x + 2
m = - ¾ , y int (0 , 2)
Ex 2 m = 9, y int (0 , -8)
y = 9x – 8
gradient Y intercept (0 ,?)
Equation of a Straight Line

4. Applying new knowledge
Line goes through (0 , 7) and is
to y = 4x + 2.
Equation?
need gradient
y intercept
perpendicular
m = - ¼ (m1m2 = -1)
y = - ¼x + 7

5. And There’s More
What angle does line 2y = 6x + 4 make
with the x axis?
m = tanθ
2y = 6x + 4
y = 3x + 2
m = 3
tanθ = 3
θ = tan-1
(3) = 71.60
m?

6. Special Cases
(annoying lines!)
x
y
Horizontal lines
m = 0
(0 , 4)
Y = 0x + 4
Y = 4

7. Special Cases
(really annoying!)
x
y
Vertical lines
m = ∞
No y
intercept!
(2 , 0)
(2 , 4)
(2 , -2)

8. Special Cases
(really annoying!)
x
y
Vertical lines
m = ∞
No y
intercept!
(2 , 0)
(2 , 4)
(2 , -2)
Equation x = 2

9. Horizontal Lines (m = 0)
are in form y = ? (i.e no x)
Vertical lines (m = ∞)
are in form x = ? (i.e no y)
Annoying Lines Equations
x
y
(0 , 5)
Y = 5
(7 , 0)
X = 7

10. Horizontal Lines (m = 0)
are in form y = ? (i.e no x)
Vertical lines (m = ∞)
are in form x = ? (i.e no y)
Annoying Lines Equations
x
y
(0 , 5)
Y = 5
(7 , 0)
X = 7