Lines parallel to the axes
There are two types of lines so simple that you do not even need a formula to write their equation: those that always stay "at the same height" and those that always stay "at the same distance to the side". They are the lines parallel to the axes.
Lines parallel to the X-axis
Write the equation of the line parallel to the x-axis (axis of abscissas $X$) passing through the point $A(3, -5)$.
Write the equation of the line parallel to the x-axis (axis of abscissas $X$) passing through the point $A(3, -5)$.
Lines parallel to the Y-axis
Write the equation of the line parallel to the y-axis (axis of ordinates $Y$) passing through the point $B(-2, 7)$.
Write the equation of the line parallel to the y-axis (axis of ordinates $Y$) passing through the point $B(-2, 7)$.
Recognising them from two points
A line passes through the points $P(4, 2)$ and $Q(-3, 2)$. Is it parallel to either of the axes? Write its equation.
A line passes through the points $P(4, 2)$ and $Q(-3, 2)$. Is it parallel to either of the axes? Write its equation.
Seeing them in the general equation
In the general equation $Ax+By+C=0$, one of the two variables is missing when the line is parallel to an axis: if $y$ is missing ($B=0$), the line is vertical; if $x$ is missing ($A=0$), it is horizontal.
Determine the value of $k$ so that the line with general equation $kx + 3y - 6 = 0$ is parallel to the $X$ axis. Write the resulting equation.
Determine the value of $k$ so that the line with general equation $kx + 3y - 6 = 0$ is parallel to the $X$ axis. Write the resulting equation.
Applications: boundaries and rectangular frames
Sports pitches, screens and architectural plans are full of lines parallel to the axes: they are the edges of any rectangle aligned with the axes.
On a football pitch, we represent the centre of the pitch at the origin of coordinates $(0,0)$. If the pitch is $100\text{ m}$ long (along the $X$ axis) and…
On a football pitch, we represent the centre of the pitch at the origin of coordinates $(0,0)$. If the pitch is $100\text{ m}$ long (along the $X$ axis) and $60\text{ m}$ wide (along the $Y$ axis), write the equations of the four straight lines that bound the pitch.
In video game development, the screen has a resolution of $1920 \times 1080$ pixels. If we place the origin $(0,0)$ in the bottom-left corner, write the equations of the…
In video game development, the screen has a resolution of $1920 \times 1080$ pixels. If we place the origin $(0,0)$ in the bottom-left corner, write the equations of the two straight lines (one horizontal and one vertical) that divide the screen into exactly four equal quadrants.
A square has its centre at point $C(3, 3)$ and its sides are parallel to the coordinate axes. If the side of the square measures $4\text{ u}$, write the equations of the…
A square has its centre at point $C(3, 3)$ and its sides are parallel to the coordinate axes. If the side of the square measures $4\text{ u}$, write the equations of the four lines containing its sides.