1Cademy - Finding the Equation of a Line Through $$(-2, -4)$$ and $$(1, -3)$$

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Finding an Equation of a Line Given Two Points

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Finding the Equation of a Line Through $(-2, -4)$ and $(1, -3)$

To find the equation of a line containing the points $(-2, -4)$ and $(1, -3)$ , apply the two-points procedure and write the result in slope-intercept form. Step $1$ — Find the slope. Apply the slope formula: $m = \frac{-3 - (-4)}{1 - (-2)}$ Subtracting a negative is equivalent to addition: $m = \frac{-3 + 4}{1 + 2} = \frac{1}{3}$ Step $2$ — Choose one point. Use $(1, -3)$ , so $x_1 = 1$ and $y_1 = -3$ . Step $3$ — Substitute into the point-slope form $y - y_1 = m(x - x_1)$ : $y - (-3) = \frac{1}{3}(x - 1)$ Simplify the left side and distribute the slope on the right: $y + 3 = \frac{1}{3}x - \frac{1}{3}$ Step $4$ — Write in slope-intercept form by subtracting $3$ from both sides: $y = \frac{1}{3}x - \frac{1}{3} - 3$ $y = \frac{1}{3}x - \frac{10}{3}$ The equation of the line is $y = \frac{1}{3}x - \frac{10}{3}$ .

Updated 2026-05-03

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OpenStax Intermediate Algebra

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