Answer:
y = –5x – 17
Step-by-step explanation:
First, we shall determine the slope of the equation y = 1/5x – 3.
The slope of the equation y = 1/5x – 3 can be obtained by comparing the equation with y = mx + c.
This is illustrated below:
y = 1/5x – 3
y = mx + c
Thus, the slope (m) of equation
y = 1/5x – 3 is 1/5
Next, we shall determine the slope of the line perpendicular to the equation as follow:
For perpendicular lines, their slope (m1 and m2) are related as follow:
m1 × m2 = –1
m1 = 1/5
1/5 × m2 = –1
m2/5 = –1
Cross multiply
m2 = 5 × –1
m2 = –5
Therefore, the slope of the line is –5.
Finally, we shall determine the equation of the line as follow:
Coordinate = (–5, 8)
x1 coordinate = –5
y1 coordinate = 8
Slope (m) = –5
y – y1 = m(x –x1)
y – 8 = –5(x – (–5))
y – 8 = –5(x + 5)
y – 8 = –5x – 25
Rearrange
y = –5x – 25 + 8
y = –5x – 17
Therefore, the equation is y = –5x – 17.
