The standard form of a line passing through the points (-1, -3) and (2, 1) is <u>4x - 3y = 5</u>.
The slope of the given line, m = (1 - (-3))/(2 - (-1)) = (1 + 3)/(2 + 1) = 4/3.
Computed using the formula for the slope of a line, m = (y₂ - y₁)/(x₂ - x₁), when a line passes through the points (x₁, y₁) and (x₂, y₂).
The point intercept form of a line is <u>y - y₁ = m(x - x₁)</u> when the line passes through the point (x₁, y₁) and has the slope m.
Thus, the given line in the point intercept form can be written as:
y - 1 = (4/3)(x - 2).
The standard form of a line is ax + by = c.
To convert the point intercept form to the standard form, we do as follows:
y - 1 = (4/3)(x - 2),
or, 3(y - 1) = 3(4/3)(x - 2) {Multiplying both sides by 3},
or, 3y - 3 = 4x - 8 {Simplifying},
or, 8 - 3 = 4x - 3y {Rearranging},
or, 4x - 3y = 5 {Rearranging and simplifying}.
Thus, the standard form of a line passing through the points (-1, -3) and (2, 1) is <u>4x - 3y = 5</u>.
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