IB Maths AI HL Sl 2 1 Straight Lines Questions

Practise IB Maths AI HL 2.1 through questions that extend line equations to parameters, intersections, geometric constraints and modelling.

Exam points

Calculate gradient and intercepts and construct or rearrange a straight-line equation from points, a graph or a stated form.
Use equal gradients to establish parallel lines and the negative-reciprocal condition to establish perpendicular lines.
Find intersections or unknown line parameters by solving simultaneous linear equations and interpret the resulting coordinates.
Check the line model by substitution, diagram geometry, domain, units and the meaning of the slope or intercept in context.

[Maximum number: 3]

The Voronoi diagram below shows four supermarkets represented by points with coordinates A(0,0), B(6,0), C(0,6) and D(2,2). The vertices X, Y, Z are also shown. All distances are measured in kilometres.

Figure for Question IB Maths AI HL Sl 2 1 Straight Lines Questions question 1 — IB Maths AI HL

The equation of (XY) is y=2-x and the equation of (YZ) is y=0.5x+3.5.
Find the coordinates of X.

identifying the correct equations to use:

y=2-x \text { and } y=2 x-7

evidence of solving their correct equations or finding points of intersection graphically

(3,-1)

Note: Accept an answer expressed as " x=3, y=-1 ".

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IB Maths AI HL Sl 2 1 Straight Lines Questions question 1