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:

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