Final answer:
The line perpendicular to the given line 3x + 9y = -8 that passes through the point P(-3, 1) has the equation y = 3x + 10.
The correct answer is option d) y=3x+10
Step-by-step explanation:
To find the equation of the line that is perpendicular to the given line and passes through the point P(-3, 1), we first need to find the slope of the given line. From the equation 3x + 9y = -8, we can rewrite it in slope-intercept form (y = mx + b) and find that the slope (m) is negative one-third (-1/3). Because perpendicular lines have slopes that are negative reciprocals of each other, the slope of our new line must be 3 (since it is the negative reciprocal of -1/3).Now that we have the slope of the perpendicular line, we can use point-slope form (y - y1 = m(x - x1)) where m is the slope and (x1, y1) is the point (-3, 1). Plugging in our values, the equation becomes y - 1 = 3(x + 3). Simplifying this, we get y - 1 = 3x + 9, and then y = 3x + 10 when we add 1 to both sides.
The correct equation for the line is y = 3x + 10, which corresponds to option d).