Linear Equations

NZ Level 7 (NZC) Level 2 (NCEA)

Parallel Lines II

Lesson

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.

Horizontal Lines

All horizontal lines are parallel to the $x$`x`-axis and all have gradients of $0$0.

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.

Vertical lines

All vertical lines are parallel to the $y$`y`-axis and their gradient is * undefined*.

Find the equation of the line $L_1$`L`1 that is parallel to the line $y=-\frac{2x}{7}+1$`y`=−2`x`7+1 and goes through the point $\left(0,-10\right)$(0,−10). Give your answer in the form $y=mx+b$`y`=`m``x`+`b`.

The lines $y=-5mx+1$`y`=−5`m``x`+1 and $y=-2+4x$`y`=−2+4`x` are parallel. Find the value of $m$`m`.

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).

Apply co-ordinate geometry techniques to points and lines

Apply co-ordinate geometry methods in solving problems