The equation of a line in the slope intercept form is expressed as
y = mx + c
Where
m represents slope
c represents y intercept
The given equation is expressed as
y = - x/3 + 5
By comparing with the slope intercept equation,
slope, m = - 1/3
If two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line. The negative reciprocal of - 1/3 is 3. Thus, the slope of the line passing through the point, (1, - 10) is 3
We would determine the y intercept, c by substituting x = 1, y = - 10 and m = 3 into the slope intercept equation. It becomes
- 10 = 3 * 1 + c
- 10 = 3 + c
c = - 10 - 3
c = - 13
We would substitute m = 3 and c = - 13 into the slope intercept equation. Thus, the equation of the line is
y = 3x - 13
Option D is correct