How are equations and geometry connected?

Key questions

1. 1

How can we use algebra to describe straight lines in the plane?

2. 2

How can we consider parallel and perpendicular lines using algebra?

3. 3

How can we translate between geometric and algebraic descriptions of lines and curves?

4. 4

How is the process of solving simultaneous equations related to geometry?

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Introducing...

Resource type Title
Building blocks Lots of lines!
Building blocks Straight lines

Developing...

Resource type Title
Building blocks Spot the difference
Many ways problem Negatively triangular
Many ways problem The circle of Apollonius... coordinate edition
Food for thought Between the lines
Food for thought Near miss
Investigation Simultaneous squares
Investigation Straight line pairs
Bigger picture Cartesian coordinates
Bigger picture The equation of a straight line

Review questions

Title Ref
A line cuts the axes to make a triangle; can we find its area? R6803
A line through a variable point creates a triangle; can we find its area? R6835
A point $Y$ moves to define a point $P$ — can we find the locus of $P\,$? R6583
Can we calculate an approximation to the root of this function? R5948
Can we find a rectangle from two vertices and a diagonal? R5967
Can we find an integer solution to three simultaneous inequalities? R5281
Can we find the area of this inscribed quadrilateral? R8471
Can we find the area of this quadrilateral? R8748
Can we find the coordinates of this tilted rectangle? R6366
Can we find the point midway between an intersection and a line? R9273
Can we find the three inequalities that define this region? R8408
Can we illustrate this pair of inequalities on a graph? R7320
Can we match this equation to its graph? R7757
Can we maximise the profit for this tractor-making business? R7642
Can we plot this graph and use it to solve two equations? R7296
Can we reflect this point in this line? R6230
Can we show that this point moves on a circle? R6234
Can we show this parallelogram is a rectangle? R8449
Given a right angle and the equations of two sides, can we find the third? R5661
If we know the sum and product of two numbers, what are they? R5887
No solutions, or infinitely many? R6514
One distance is double another; can we find a locus? R8080
What is the largest $x$ to satisfy these three inequalities? R9709
What's the locus of the intersection of these variable lines? R5255
Where is the foot of the perpendicular from a point to a line? R5202
Which four inequalities define this region? R5737
Which of these graphs shows the area $A(c)$ as $c$ varies? R9617