Find the equation in standard form of the line passing through the points (2, -3) and (4, 2)

Solution:

The standard form of an equation of line is given by:

y = mx + c

The point slope form is

y - y₁ = m (x - x₁)

Where m is the slope,

(x₁, y₁) is the point through which the given line passes.

The slope formula is given by:

m = (y₂ - y₁) / (x₂ - x₁)

Substituting the values

m = (2 - (-3)) / (4 - 2)

m = 5/2

So we get

y - (-3) = 5/2 (x - 2)

By using the distributive property

y + 3 = 5/2 (x - 2)

Multiplying 2 on both sides, we get

2y + 6 = 5x - 10

Subtracting 6 on both sides, we get

2y + 6 - 6 = 5x - 10 - 6

2y = 5x - 16

On rearranging, we get

5x - 2y = 16

Therefore, the equation in standard form is 5x - 2y = 16.

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Find the equation in standard form of the line passing through the points (2, -3) and (4, 2)

Summary:

The equation in standard form of the line passing through the points (2, -3) and (4, 2) is 5x - 2y = 16.