Question:
What is the equation of a line passing through the two points \((41,11)\) and \((4,-9)\)?
What is the equation of a line passing through the two points \((41,11)\) and \((4,-9)\)?
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When the slope is fractional, give an exact fractional equation or move to standard form \(Ax + By + C = 0\) to avoid decimals.
Updated On: Oct 3, 2025
- \(y = 2027x - 1415\)
- \(y = 1714x - 14825\)
- \(y = 2037x - 41337\)
- \(y = 14x - 18\)
- \(20x - 37y - 413 = 0\)
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Solution and Explanation
Step 1: Find the slope.
\(m = \dfrac{11 - (-9)}{41 - 4} = \dfrac{20}{37}\).
Step 2: Use point–slope form with \((41,11)\).
\(y - 11 = \dfrac{20}{37}(x - 41)\).
Step 3: Simplify to slope–intercept form.
\(y = \dfrac{20}{37}x - \dfrac{820}{37} + 11 = \dfrac{20}{37}x - \dfrac{820 - 407}{37} = \dfrac{20}{37}x - \dfrac{413}{37}\).
Step 4: Standard form (optional).
Multiply by 37: \(37y = 20x - 413 \Rightarrow 20x - 37y - 413 = 0\).
Final Answer:
\[ \boxed{\,y = \frac{20}{37}x - \frac{413}{37}\,} \]
\(m = \dfrac{11 - (-9)}{41 - 4} = \dfrac{20}{37}\).
Step 2: Use point–slope form with \((41,11)\).
\(y - 11 = \dfrac{20}{37}(x - 41)\).
Step 3: Simplify to slope–intercept form.
\(y = \dfrac{20}{37}x - \dfrac{820}{37} + 11 = \dfrac{20}{37}x - \dfrac{820 - 407}{37} = \dfrac{20}{37}x - \dfrac{413}{37}\).
Step 4: Standard form (optional).
Multiply by 37: \(37y = 20x - 413 \Rightarrow 20x - 37y - 413 = 0\).
Final Answer:
\[ \boxed{\,y = \frac{20}{37}x - \frac{413}{37}\,} \]
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