A line passes through the point (2,-5) and is perpendicular to the line with the equation y = 1/5x+ 5. What's the equation of the line?
OA) y= -1/5x+1
B) y=1/5x+4
C) y = 5x - 2
OD) y = -5x + 5

D) y = -5x + 5

Step-by-step explanation:

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

The first line is y = 1/5x + 5. Its slope is 1/5. A line parallel/perpendicular to this one will have a slope of -5.

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

y = -5x + b

To find b, we want to plug in a value that we know is on this line: in this case, it is (2, -5). Plug in the x and y values into the x and y of the standard equation.

-5 = -5(2) + b

To find b, multiply the slope and the input of x (2)

-5 = -10 + b

Now, add 10 to both sides to isolate b.

5 = b

Plug this into your standard equation.

y = -5x + 5

This equation is parallel/perpendicular to your given equation (y = 1/5x + 5) and contains point (2, -5)

Hope this helps!