Final answer:
To find the equation of a line perpendicular to x + 3y = -3 and passes through the point (4,2), you need to determine the slope of the given line and use it to find the slope of the perpendicular line. The equation of the perpendicular line is y = 3x - 10.
Step-by-step explanation:
To find the equation of a line that is perpendicular to the given line, we need to determine the slope of the given line and use it to find the slope of the perpendicular line.
The given line equation is x + 3y = -3. Solving for y, we get y = (-1/3)x - 1.
The slope of the given line is -1/3. The slope of a line perpendicular to it can be found using the formula: slope = -1/slope of given line. So, slope of perpendicular line = -1/(-1/3) = 3.
Now, we have the slope of the perpendicular line, and we also have a point (4,2) that the line passes through. Using the point-slope form of a line, y - y1 = m(x - x1), we can substitute the values and get the equation of the perpendicular line:
y - 2 = 3(x - 4)
y - 2 = 3x - 12
y = 3x - 10