Consider the system of equations shown here. y is equal to negative 5 x plus 1 y is equal to negative 5 x plus 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?
Answer
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 different slopes but the same y -intercept.
D
The linear equations have the same slope but different y -intercepts.
Explanation
Both equations are in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. Each equation has slope −5, but their y-intercepts are 1 and 10. Lines with the same slope and different y-intercepts are parallel, so the correct choice is “The linear equations have the same slope but different y-intercepts.”
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