What could be the equation of a line that is perpendicular to the line represented by 2x - y = 7?

Solution:

Given, the equation of the line is 2x - y = 7.

We have to find the equation of the line that is perpendicular to the given line.

The equation of the line in slope-intercept form is given by

y = mx + b -------------- (1)

Where, m is the slope

b is the y intercept

If two lines are perpendicular to each other

m₁ . m₂ = -1 …. (2)

From the equation 2x - y = 7

m₁ = 2

Substituting the values in (2)

2 . m₂ = -1

m₂ = -1/2

If the line is perpendicular to 2x - y = 7

As the y intercept value is not given

Consider the y intercept as d

y = -1/2 x + d

Therefore, the equation of the line is y = -1/2 x + d

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What could be the equation of a line that is perpendicular to the line represented by 2x - y = 7?

Summary:

The equation of a line that is perpendicular to the line represented by 2x - y = 7 is y = (-1/2)x + d.