<line>

<line> is a Graphical component that renders a line when nested inside a <graph> component, and renders an equation otherwise.

Current functionality supports generation of lines in $\mathbb{R^2}$ through user-specification of:

1. a single pair of points
2. through a single point and a specified slope
3. with an equation, or <function>

Attributes and Properties

Example: Default <line>

The default <line> without any attributes specified (other than a styleNumber) is illustrated. This line is not very interesting; it is just the $x$-axis. The equation of the line is copied below the <graph>. You can click and drag the line to see this equation updated.

Example: <line> with slope and through point

Two lines are graphed using both the slope and through attributes.

Example: <line> through 2 points

Two lines are graphed by specifying two through points using the through attribute.

Example: <line> by equation

Two lines are graphed by providing their equations directly.

Example: Line as a <function>

Two lines are defined using the <function> component. This is a useful alternative to defining a line with the <line> component if the function needs to be evaluated at different input values.

Attribute Example: through

<graph size="small">
  <line name="line1" slope="-3" through="(-1,1) (8,4)" />
  <point name="A" styleNumber="2">(-6,-2)</point>
  <point name="B" styleNumber="2">(5,3)</point>
  <line name="line2" through="$A $B" styleNumber="2"/> 
</graph>  
<p>Line 1 <c>equation</c>: $line1.equation</p>
<p>Line 2 <c>equation</c>: $line2.equation</p>

Two lines are graphed by specifying two through points using the through attribute.

Attribute Example: slope

<slider name="m" labelIsName from="-10" to="10"/>
<graph size="small">
  <line name="line1" slope="$m"/>
</graph>
<p><c>slope</c>: $line1.slope</p>      

If only the slope attribute is specified, the $y$-intercept defaults to $(0,0)$.

Attribute Example: equation

<p>Enter an equation for a line (use variables <m>x, y</m>):
  <mathInput name="userEq"/></p>
<graph size="small">
  <line name="line1" equation="$userEq"/>
</graph>
<p><c>equation</c>: $line1.equation</p>

The equation attribute takes any linear expression in $x$ and $y$, unless the variables attribute is also employed.

Attribute Example: variables

The variables attribute allows customization of the independent and dependent variable names.

Attribute Example: Standard graphical attributes

The uses of the following standard graphical attributes are illustrated: hide, draggable, layer, styleNumber, applyStyleToLabel and labelIsName.

Property Example: Attributes as properties

The above listed attributes of a named <line> are also available as properties.

Property Example: points

The points property of a named <line> returns the through points of the line in an array.

Property Example: xIntercept, yIntercept

The xIntercept and yIntercept properties return the intercepts of the named <line>.

Property Example: coeff0, coeffVar1, coeffVar2

Linear coefficients corresponding to the linear form $A x + B y + C = 0$ can be obtained with the above properties, where $C =$coeff0, $B =$coeffVar2 and $A =$coeffVar1.

Property Example: latex

The latex property renders the latex code for rendering the equation of the line.