Study lines in the number plane. Consider the gradient and y-intercept and relate them to the equation of the line.
Explore the effect of translation. Compare the two forms of the equation of a line.
Line Explorer
Investigate the slope, intercepts and equations of lines
Adjust the constraints and drag the points to explore the graphs and equations of a
variety of lines.
Standard form:
Gradient-intercept form:
Interactively study straight lines
Drag either of the blue points on the line.
The resulting change in the line depends on the constraint setting:
None
The points may be dragged anywhere, redefining the line,
X
The x coordinate of each point is fixed, so movement is only up or down,
Y
The y coordinate of each point is fixed, so movement is only left or right,
X + Y
The point moves only along the current line.
Clicking and dragging the line itself allows translation of the line.
If Intercepts is selected, the X and Y intercepts are shown in green.
Values are shown as fractions or decimals according to the state of the
Decimals setting.
The equation of the current line is constantly displayed and updated
as points are moved. Alternatively it can be entered using the Enter equation…
dialog in either standard form, i.e. x - 2y + 4 = 0 or in gradient-intercept form, i.e.
y = 1/2x + 2.
Click and hold the chart background to bring up a magnifier.
Enter an equation for a line:
Use the form ay = bx + c,
e.g. y = 2x - 5 or 3y = -x + 6