NZ Level 7 (NZC) Level 2 (NCEA)
Parallel Lines II
Lesson

## 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.

Horizontal Lines

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.

Vertical lines

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):

1. Find the gradient of the given line.

2. 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).

### Outcomes

#### M7-1

Apply co-ordinate geometry techniques to points and lines

#### 91256

Apply co-ordinate geometry methods in solving problems