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Consider the system of equations shown below.

y = negative 5 x + 1. y = negative 5 x + 10

When graphed, the system consists of two lines that will never meet, no matter how far they are extended. Why are the lines parallel?
A. The linear equations have the same slope and y-intercept.
B. The linear equations have different slopes and y-intercepts.
C. The linear equations have the same slope but different y-intercepts.
D. The linear equations have different slopes but the same y-intercept.

1 answer

The lines represented by the equations \( y = -5x + 1 \) and \( y = -5x + 10 \) have the following characteristics:

  • Both equations have the same slope of \(-5\).
  • However, they have different y-intercepts (1 and 10, respectively).

Since they have the same slope but different y-intercepts, the lines are parallel and will never intersect.

The correct answer is: C. The linear equations have the same slope but different y-intercepts.