Question

You just looked at the graph of this system of equations. Why will the lines never intersect? y = –x + 5 y = –x – 3

Answer 1

Sample Response:

The linear equations have the same slope, so the rate of change for each is the same. As long as the rate of change is the same, the lines will stay the same distance apart and not intersect.

Answer 2

The lines are parallel

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - x + 5 is in this form with m = - 1

y = - x - 3 is in this form with m = - 1

Parallel lines have equal slopes

The 2 lines are parallel and never intersect.