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What is the slope of a line that is perpendicular to the line
y = 2x – 6?

1 Answer

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Answer:

The slope of a line that is perpendicular to the line y = 2x – 6 is -1/2.

Explanation:

The slope-intercept form of the line equation


y = mx+b

where


  • m is the slope

  • b is the y-intercept

Step 1:

Finding the slope of the given equation

The given equation is


y = 2x - 6

comparing with the slope-intercept form of the line equation

The slope of the equation is: m = 2

Step 2:

Determining the slope of the perpendicular line

In Mathematics, a line perpendicular to another line has a slope that is the negative reciprocal of the slope of the other line.

  • As the slope of the equation is: m = 2

Therefore, the slope of the new perpendicular line:


-(1)/(m)=-(1)/(2)

Hence, the slope of a line that is perpendicular to the line y = 2x – 6 is -1/2.

Important Tip:

  • The product of the slopes of perpendicular lines is -1.

Verification:

The slope of the given line:


m_1=2

The slope of the perpendicular line:


m_2=-(1)/(2)\:\:\:\:

The product of the slopes is:


\:m_1* \:m_2\:=2* -(1)/(2)\:\:=-1

As the product of the slopes of perpendicular lines is -1, therefore, the lines are perpendicular.

Thus, the slope of a line that is perpendicular to the line y = 2x – 6 is -1/2.

User PabloG
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