What is the equation of the line perpendicular to -x + y = 7 and passing through (-1, -1)?

Solution:

It is given that

The equation of the line perpendicular to -x + y = 7 and passing through (-1, -1).

Now we have to find the slope of the given line -x + y = 7,

y = x + 7

y = m₁x + c

Slope is m₁ = 1

Then the product of slopes of two perpendicular lines is,

m₁ × m₂ = -1

By cross multiplication we get,

m₂ = -1/m₁

Substituting the values,

m₂ = -1/1

m₂ = -1

So equation of line in point (-1, -1) slope from is,

y - y₁ = m₂ (x - x₁)

y + 1 = -1 (x + 1)

y + 1 = -(x + 1)

Therefore, the equation of the line is y + 1 = -(x + 1).

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What is the equation of the line perpendicular to -x + y = 7 and passing through (-1, -1)?

Summary:

The equation of the line perpendicular to -x + y = 7 and passing through (-1, -1) is y + 1 = -(x + 1).