What is the equation of the line that passes through (-2, 2) and (1, -4)?

Solution:

The points given are (-2, 2) and (1, -4)

We know that slope can be found using the formula

m = (y₂ - y₁)/ (x₂ - x₁)

Substituting the values

m = (-4 - 2)/ (1 - (-2))

By further calculation

m = -6/3

m = -2

The point slope formula is

y - y₁ = m (x - x₁)

Let us use the point (-2, 2)

Substituting the values

⇒ y - 2 = -2 (x - (-2))

⇒ y - 2 = -2 (x + 2)

⇒ y - 2 = -2x - 4

⇒ y + 2x = -4 + 2

⇒ 2x + y = -2

Therefore, the equation of the line is 2x + y = -2.

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What is the equation of the line that passes through (-2, 2) and (1, -4)?

Summary:

The equation of the line that passes through (-2, 2) and (1, -4) is 2x + y = -2.