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IB Maths AI SL 2.1 Straight lines

IB Maths AI SL 2.1 Straight lines
IB Mathematics: applications and interpretation guide, first assessment 2021

Students practise calculating gradients and intercepts of straight lines from coordinates or context, writing equations in gradient–intercept or point–gradient form, and…

How this is tested

  • calculate gradient as (y₂ − y₁)/(x₂ − x₁) for points on a ray of light or edge between sites
  • write a line equation using point-gradient form or a perpendicular bisector
  • read the y-intercept directly from the constant term or from the graph

Question 4(a)

[Maximum number: 1]

Jenny designs a flexible suspension bridge, spanning 10 metres over the Swinburne Creek.
Jenny believes that when no people are on the bridge, the height, y, of the walkway on the bridge above the creek can be modelled by

y=ax2+bx+c for 0≤x≤10.y=a x^{2}+b x+c \text { for } 0 \leq x \leq 10 .

She uses a coordinate system where the origin is directly below one side of the bridge, as shown in the following diagram. All distances are measured in metres.

According to this model, the points P(0,4), Q(2,3.936) and R(5,3.9) will be located on the walkway of the bridge. Point R is the lowest point of the bridge.

Figure for Question 4(a) — IB Maths AI SL

Write down the value of c, the y-intercept of the model.

Using point Q , Jenny finds the equation -0.064=4 a+2 b.