Consider the system of equations shown below. y=-5x+1 y=-5x+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? The linear equations have the same slope and y-intercept. The linear equations have different slopes and y-intercepts. The linear equations have the same slope but different y-intercepts. The linear equations have different slopes but the same y-intercept.

The correct answer is: The linear equations have the same slope but different y-intercepts.<br /><br />Explanation: The given system of equations consists of two linear equations:<br /><br />$y = -5x + 1$<br />$y = -5x + 10$<br /><br />To determine why the lines are parallel, we need to compare the slopes and y-intercepts of the two equations.<br /><br />The slope of a linear equation in the form $y = mx + b$ is the coefficient of $x$, which is $m$. In this case, both equations have the same slope of $-5$.<br /><br />The y-intercept of a linear equation in the form $y = mx + b$ is the constant term $b$. In this case, the first equation has a y-intercept of $1$, while the second equation has a y-intercept of $10$.<br /><br />Since the two equations have the same slope but different y-intercepts, the lines represented by these equations will be parallel. Parallel lines have the same slope but different y-intercepts, which means they will never intersect or meet, no matter how far they are extended.