Final answer:
The equation of the line perpendicular to 3x - 5y = 6 and passing through P(-8,0) is y = (-5/3)x + 40/3.
Step-by-step explanation:
To write an equation of a line that passes through point P(-8,0) and is perpendicular to the given line 3x - 5y = 6, we need to find the slope of the given line and then use the negative reciprocal of that slope for our perpendicular line. Start by solving the given equation for y to get it into slope-intercept form (y = mx + b), where m represents the slope. The given equation can be rewritten as:
y = (3/5)x - 6/5
The slope of the given line is 3/5. The slope (m) of the line perpendicular to this would be the negative reciprocal, so m = -5/3. Now, using the point-slope form of a line equation, which is y - y1 = m(x - x1), where (x1, y1) are the coordinates of the given point, we can plug in our values:
y - 0 = (-5/3)(x - (-8))
Simplifying the equation, we get:
y = (-5/3)x - (-5/3)(-8)
y = (-5/3)x + 40/3
Therefore, the equation of the line perpendicular to 3x - 5y = 6 and passing through point P(-8,0) is:
y = (-5/3)x + 40/3