Question

What is the equation of the line that is parallel to the line y = -1/3 x + 4 and passes through the point (6, 5)?a) y = -1/3x + 3b) y = -1/3x + 7c) y = 3x – 13d) y = 3x + 5

Answer 1

Note that the slope of parallel lines are always equal.

From the given line :

`y=-(1)/(3)x+4`

The slope is m = -1/3 and we need the equation of the line that passes through (6, 5)

Using point-slope formula :

`\begin{gathered} y-y_1=m(x-x_1) \\ y-5=-(1)/(3)(x-6) \\ y-5=-(1)/(3)x+2 \\ y=-(1)/(3)x+2+5 \\ y=-(1)/(3)x+7 \end{gathered}`

The answer is B.