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

Answer:

$m_1 = m_2 = 4$

Step-by-step 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