Parallel Lines II
Parallel to an axis
Horizontal Lines
Horizontal lines are lines where the $y$y value is always the same.
Let's look at the coordinates for A,B and C on this line.
$A=\left(-4,4\right)$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, $y=4$y=4.
This means that regardless of the $x$x-value the $y$y value is always 4.
The equation of this line is $y=4$y=4
So if an equation of a straight line is $y=b$y=b, then it will be a horizontal line at the point where $y=b$y=b.
The $x$x-axis itself is a horizontal line. The equation of the $x$x-axis is $y=0$y=0.
All horizontal lines are parallel to the $x$x-axis and all have gradients of $0$0.
Vertical Lines
Vertical Lines are lines where the $x$x-value is always the same.
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-coordinates are the same, $x=5$x=5.
This means that regardless of the $y$y-value the $x$x-value is always $5$5.
The equation of this line is $x=5$x=5
So if an equation of a straight line is $x=b$x=b, then it will be a vertical line at the point where $x=b$x=b.
The $y$y-axis itself is a vertical line. The equation of the $y$y-axis is $x=0$x=0.
All vertical lines are parallel to the $y$y-axis and their gradient is undefined.
Examples
Question 1
Find the equation of the line $L_1$L1 that is parallel to the line $y=-\frac{2x}{7}+1$y=−2x7+1 and goes through the point $\left(0,-10\right)$(0,−10). Give your answer in the form $y=mx+b$y=mx+b.
Question 2
The lines $y=-5mx+1$y=−5mx+1 and $y=-2+4x$y=−2+4x are parallel. Find the value of $m$m.
Question 3
A line goes through A$\left(-2,9\right)$(−2,9) and B$\left(-4,-4\right)$(−4,−4):
Find the gradient of the given line.
Find the equation of a line that has a $y$y-intercept of $-5$−5 and is parallel to the line that goes through A$\left(-2,9\right)$(−2,9) and B$\left(-4,-4\right)$(−4,−4).