Straight lines on the Cartesian Plane can literally be in any direction and pass through any two points.
This means that straight lines can be:
$Gradient=\frac{rise}{run}$Gradient=riserun
On horizontal lines, the $y$y value is always the same for every point on the line. In other words, there is no rise- it's completely flat.
$A=\left(-4,4\right)$A=(−4,4)
$B=\left(2,4\right)$B=(2,4)
$C=\left(4,4\right)$C=(4,4)
All the $y$y-coordinates are the same. Every point on the line has a $y$y value equal to $4$4, regardless of the $x$x-value.
The equation of this line is $y=4$y=4.
Since gradient is calculated by $\frac{\text{rise }}{\text{run }}$rise run and there is no rise (ie. $\text{rise }=0$rise =0), the gradient of a horizontal line is always $0$0.
On vertical lines, the $x$x value is always the same for every point on the line.
Let's look at the coordinates for A,B and C on this line.
$A=\left(5,-4\right)$A=(5,−4)
$B=\left(5,-2\right)$B=(5,−2)
$C=\left(5,4\right)$C=(5,4)
All the $x$x-coordinates are the same, $x=5$x=5, regardless of the $y$y value.
The equation of this line is $x=5$x=5.
Vertical lines have no "run" (ie. $\text{run }=0$run =0). l If we substituted this into the $\frac{\text{rise }}{\text{run }}$rise run equation, we'd have a $0$0 as the denominator of the fraction. However, fractions with a denominator of $0$0 are undefined.
So, the gradient of vertical lines is always undefined.
Linear equations can be written in the form $y=mx+b$y=mx+b, where $m$m is the gradient.
Notice how the equations of horizontal and vertical lines are not written in this form. Neither of them have a coefficient of $x$x.
What is the gradient of any line parallel to the $x$x-axis?
$A$A $\left(2,1\right)$(2,1), $B$B $\left(7,3\right)$(7,3) and $C$C $\left(7,-5\right)$(7,−5) are the vertices of a triangle.
Which side of the triangle is a vertical line?
$BC$BC
$AB$AB
$AC$AC
Determine the area of the triangle using $A=\frac{1}{2}bh$A=12bh.