Question

Explain why you cannot find the intersection points of the two lines shown below. Give both an algebraic reason and a graphical reason. y=4x+1 and y= 4x+10

Answer 1

`m_1 = m_2 = 4`

Explanation:

Given

`y = 4x + 1`

`y = 4x + 10`

Required

Show that these two lines have no point of intersection

The general equation of a line is

`y = mx + b`

Where m represents slope

In
`y = 4x + 1`

`m = 4`

Similarly; in
`y = 4x + 10`

`m = 4`

Since the slope of both lines are equal;

`m_1 = m_2 = 4`

This implies that the lines are parallel and parallel lines have no point of intersection

See Attachment for Graph