LINE IT UP
Use the widget 'The line is drawn' to explore the link between the graph of a line and its equation.
TASK 1
Locking the slope
Drag one handle so that it lies on the y-axis at –2.
Click the button for
to view one form of the equation.
Grab the line (not on a handle) and slide the line up and down leaving the
handle on the y-axis without changing the slope of the line.
a As you move the line, what part of the
does not change? ______________________
b What part of the equation does change? ______________________________________________
c Comment on what you have discovered.
______________________________________________________________________________
TASK 2
Locking the y-intercept
Move one handle back to the y-axis at –2.
a Drag the other handle to (3, 4) then click
and
to record the
gradient and the equation of the new line.
Gradient =
Equation is:
y=
b Drag the top handle to (–2, 4) and again
record the
and
.
Gradient =
Equation is:
y=
c Comment on what you have discovered.
______________________________________________________________________________
Continue to explore by changing the line on the widget and comparing the
and the
.
,
TASK 3
Interpret equations
There are four equations given below. Use the widget and your discoveries from tasks 1 and 2 to create
each line. Draw a sketch of each and mark the position you have used of the two handles. Can the two
handles be placed in more than one position for each line?
a y = 2x – 3
b y = –3x + 2
c y= 1 x+1
y = –5x
2
TASK 4
Meet the specs
Write the equation of each line then check your answer by using the widget to create the line.
a Gradient 1 and y-intercept –3
____________________________________________________
b Gradient –1 and y-intercept 0
____________________________________________________
c Gradient 0 and y-intercept 4
____________________________________________________
d Gradient 2 and y-intercept –2
___________________________________________________
3