Core Chapter 1: Straight Lines

Question 1

How is a line’s gradient measured?

Answer 1

rise/run = y₂- y₁/x₂- x₁

Question 2

What are a line’s x-intercepts and y-intercepts?

Answer 2

x-intecept: y=0
y-intercept: x=0

Question 3

What are the 2 different types of lines?

Answer 3

Parallel lines: same gradient
(m₁=m₂)
Perpendicular lines: gradients are negative reciprocals of each other
(m₁= -1/m₂)

Question 4

What are the 3 different forms of an equation of a straight line?

Answer 4

1) Gradient-intercept form
(y = mx + c)
- When the gradient (m) and y-intercept (c) is known

2) Point-gradient form
(y-y₁/x-x₁=m)
(y-y₁=m(x-x₁)
- When coordinates of 1 point (x₁, y₁) and the gradient (m) is known

3) General form (ax + by + d = 0)
- Rearranged using other forms

Question 5

What is a perpendicular bisector?
How can the equation of the perpendicular bisector be found?

Answer 5

Perpendicular bisector:
1) Perpendicular to the line
(gradient is negative reciprocal to the line’s gradient)
2) Passes through the line’s midpoint (x₁+x₂/2, y₁+y₂/2)

Equation of a perpendicular bisector:
1) Find mid-point of the line (intersection between the line and its perpendicular bisector)
2) Find gradient of the line
3) Find gradient of the perpendicular bisector
4) Apply point-gradient form