Find an equation of the line through the pair of points. Write the equation in the form Ax + By = C.
-$( 10,2 )$ and $( - 1 , - 4 )$
A) $8 x + 3 y = - 4$
B) $- 6 x + 11 y = - 38$
C) $- 8 x - 3 y = - 4$
D) $6 x + 11 y = - 38$

Question

Quizplus · Accepted Answer

To find the equation of the line through the points $(10,2)$ and $(-1,-4)$, we first calculate the slope $m$ using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$, which gives us $m = \frac{-4 - 2}{-1 - 10} = \frac{-6}{-11} = \frac{6}{11}$. Then, using point-slope form $y - y_1 = m(x - x_1)$ with one of the points, say $(10,2)$, we get $y - 2 = \frac{6}{11}(x - 10)$. Multiplying through by 11 to clear the fraction gives $11(y - 2) = 6(x - 10)$, which simplifies to $11y - 22 = 6x - 60$. Rearranging to the form $Ax + By = C$, we get $-6x + 11y = -38$, which matches option B.

Find an Equation of the Line Through the Pair of Points