Which is the equation of the line through the point (−3, 8) that is perpendicular to the line y=14x+12?

y = -1/14x + 109/14

Step-by-step explanation:

If two lines are perpendicular to each other, they have opposite slopes.

The first line is y = 14x + 12. Its slope is 14. A line perpendicular to this one will have a slope of -1/14.

Plug this value (-1/14) into your standard point-slope equation of y = mx + b.

y = -1/14x + b

To find b, we want to plug in a value that we know is on this line: in this case, it is (-3, 8). Plug in the x and y values into the x and y of the standard equation.

8 = -1/14(-3) + b

To find b, multiply the slope and the input of x (-3)

8 = 3/14 + b

Now, subtract 3/14 from both sides to isolate b.

8 - 3/14 = b

112/14 - 3/14 = b

109/14 = b

Plug this into your standard equation.

y = -1/14x + 109/14

This equation is parallel/perpendicular to your given equation (y = 14x + 12) and contains point (-3, 8)

Hope this helps!

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