Write an equation of the line that passes through ( − 8 , 5 2 ) \left( - 8 , \frac { 5 } { 2 } \right) ( − 8 , 2 5 ) and has a slope of m = 1 6 m = \frac { 1 } { 6 } m = 6 1 .A) − x + 6 y = − 38 - x + 6 y = - 38 − x + 6 y = − 38 B) − x + y = − 38 - x + y = - 38 − x + y = − 38 C) x + 6 y = − 41 x + 6 y = - 41 x + 6 y = − 41 D) − x + 6 y = 23 - x + 6 y = 23 − x + 6 y = 23 E) − x + 6 y = − 23 - x + 6 y = - 23 − x + 6 y = − 23

Question

Write an equation of the line that passes through   ( − 8 , 5 2 )  \left( - 8 , \frac { 5 } { 2 } \right)  ( − 8 , 2 5 ​ )    and has a slope of   m = 1 6 m = \frac { 1 } { 6 } m = 6 1 ​   .A)    − x + 6 y = − 38 - x + 6 y = - 38 − x + 6 y = − 38 B)    − x + y = − 38 - x + y = - 38 − x + y = − 38 C)    x + 6 y = − 41 x + 6 y = - 41 x + 6 y = − 41 D)    − x + 6 y = 23 - x + 6 y = 23 − x + 6 y = 23 E)    − x + 6 y = − 23 - x + 6 y = - 23 − x + 6 y = − 23

Francy Blanc · Accepted Answer

Final Answer : D, Explanation :   We can use point-slope form to start: y − y 1 = m ( x − x 1 ) y - y_1 = m(x - x_1) y − y 1 ​ = m ( x − x 1 ​ ) where   ( x 1 , y 1 ) = ( − 8 , 5 / 2 ) (x_1, y_1) = (-8, 5/2) ( x 1 ​ , y 1 ​ ) = ( − 8 , 5/2 )   and   m = 1 / 6 m = 1/6 m = 1/6  . Plugging in these values, we get y − 5 2 = 1 6 ( x + 8 ) y - \dfrac{5}{2} = \dfrac{1}{6}(x + 8) y − 2 5 ​ = 6 1 ​ ( x + 8 ) Multiplying both sides by 6 to get rid of the fraction, we get 6 y − 15 = x + 8 6y - 15 = x + 8 6 y − 15 = x + 8 Rearranging, we get x − 6 y = − 23 x - 6y = -23 x − 6 y = − 23 So the answer is (D).

Write an equation of the line that passes through $\left( - 8 , \frac { 5 } { 2 } \right)$ and has a slope of $\frac { 1 } { 6 }$ .

A) $- x + 6 y = - 38$
B) $- x + y = - 38$
C) $x + 6 y = - 41$
D) $- x + 6 y = 23$
E) $- x + 6 y = - 23$

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