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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

What is the equation of the line that is parallel to the line y 13 x 4 and passes through the point 6 5a y 13x 3b y 13x 7c y 3x 13d y 3x 5 class=


Answer :

Note that the slope of parallel lines are always equal.

From the given line :

[tex]y=-\frac{1}{3}x+4[/tex]

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

Using point-slope formula :

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

The answer is B.

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