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

Question

Quizplus · Accepted Answer

We can use point-slope form to start:

$$y - y_1 = m(x - x_1)$$

where $(x_1, y_1) = (-8, 5/2)$ and $m = 1/6$. Plugging in these values, we get

$$y - \dfrac{5}{2} = \dfrac{1}{6}(x + 8)$$

Multiplying both sides by 6 to get rid of the fraction, we get

$$6y - 15 = x + 8$$

Rearranging, we get

$$x - 6y = -23$$

So the answer is (D).

Write an Equation of the Line That Passes Through (−8,52)\left( - 8 , \frac { 5 } { 2 } \right)(−8,25​)

Write an Equation of the Line That Passes Through $\left( - 8 , \frac { 5 } { 2 } \right)$