Linear functions and graphs

problem
Surprising transformations

Age

14 to 16

Challenge level

I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?
problem
Translating lines

Age

11 to 14

Challenge level

Investigate what happens to the equation of different lines when you translate them. Try to predict what will happen. Explain your findings.
problem
Four on the road

Age

14 to 16

Challenge level

Four vehicles travel along a road one afternoon. Can you make sense of the graphs showing their motion?
problem
Reflecting lines

Age

11 to 14

Challenge level

Investigate what happens to the equations of different lines when you reflect them in one of the axes. Try to predict what will happen. Explain your findings.
problem
At right angles

Age

14 to 16

Challenge level

Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?
problem
Spot the difference

Age

16 to 18

Challenge level

If you plot these graphs they may look the same, but are they?
problem
Negatively triangular

Age

14 to 16

Challenge level

How many intersections do you expect from four straight lines ? Which three lines enclose a triangle with negative co-ordinates for every point ?
problem
Graphical triangle

Age

14 to 16

Challenge level

What is the area of the triangle formed by these three lines?
problem
Perpendicular lines

Age

14 to 16

Challenge level

Position the lines so that they are perpendicular to each other. What can you say about the equations of perpendicular lines?
problem
Parallel lines

Age

11 to 14

Challenge level

How does the position of the line affect the equation of the line? What can you say about the equations of parallel lines?