Question

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 = -5x + 5
OC) y = 5x - 2
D) y=1/5x+4

Answer 1

Answer: B) y = -5x+5

slope = -5, y intercept = 5

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Explanation:

The given equation has slope 1/5. We can see that by comparing it to y = mx+b, with m as the slope.

Flip the fraction and the sign to go from 1/5 to -5/1 = -5. The perpendicular slope is -5. We can stop here since only choice B has such a slope.

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If you're curious about finding the y intercept, then you would use m = -5 along with (x,y) = (2,-5) to find the value of b

y = mx+b

-5 = -5(2)+b

-5 = -10+b

-5+10 = -10+b+10 ... adding 10 to both sides

5 = b

b = 5 is the y intercept

So we have y = mx+b update to y = -5x+5 as the perpendicular line.

Answer 2

Answer:

$y = - 5x + 5$

Step-by-step explanation:

$y = \frac{1}{5} x + 5 \\ m = \frac{1}{5} \\ m1 = \frac{ - 1}{m2}$

.

$\frac{1}{5} = \frac{ - 1}{m2 } \\ m2 = - 5 \\ x = 2 \: y = - 5$

$y = mx + c \\ - 5 = - 5(2) + c \\ - 5 = - 10 + c \\ - 5 + 10 = c$

$c = 5 \\ m = - 5 \\ y = mx + c \\ y = - 5x + 5$