Question

Decide if the two lines y =1/5x + 3 and y = 5x – 2 are parallel, perpendicular, or neither. Explain your answer.

Answer 1

The given equation of lines are:

`y=(1)/(5)x+3;\; y=5x-2`

Notice that the equations of the lines are given in the slope-intercept form y=mx+c, where m is the slope and c is the y-intercept.

Comparing with the given equation, it follows that the slopes of the given lines are:

`m_1=(1)/(5);\; m_2=5`

Recall that the slopes of perpendicular lines are negative reciprocals of each other.

Recall also that the slopes of parallel lines are equal.

Notice that the slopes of the given lines, 1/5 and 5 are just reciprocals of each other.

Hence, they are neither perpendicular lines nor parallel lines because their slopes are reciprocals of each other.

Answer:

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