1Cademy - Finding the Equation of a Line Through $$(-3, -1)$$ and $$(2, -2)$$

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Finding an Equation of a Line Given Two Points

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Finding the Equation of a Line Through $(-3, -1)$ and $(2, -2)$

To find the equation of a line containing the points $(-3, -1)$ and $(2, -2)$ , apply the four-step two-points procedure and write the result in slope-intercept form. Step $1$ — Find the slope. Apply the slope formula: $m = \frac{-2 - (-1)}{2 - (-3)} = \frac{-1}{5} = -\frac{1}{5}$ Step $2$ — Choose one point. Use $(2, -2)$ , so $x_1 = 2$ and $y_1 = -2$ . Step $3$ — Substitute into the point-slope form $y - y_1 = m(x - x_1)$ : $y - (-2) = -\frac{1}{5}(x - 2)$ Simplify the left side and distribute $-\frac{1}{5}$ on the right: $y + 2 = -\frac{1}{5}x + \frac{2}{5}$ Step $4$ — Write in slope-intercept form by subtracting $2$ from both sides: $y = -\frac{1}{5}x + \frac{2}{5} - 2$ $y = -\frac{1}{5}x - \frac{8}{5}$ The equation of the line is $y = -\frac{1}{5}x - \frac{8}{5}$ . This example illustrates how subtracting a negative coordinate ( $y - (-2)$ ) becomes addition, and how a fractional slope produces fractional terms throughout the calculation.

Updated 2026-05-03

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