Final answer:
To find the equation of a line that is perpendicular to x + 3y = -3 and passes through the point (4,2), determine the slope of the given line, find the negative reciprocal of that slope, and use the point-slope form of a linear equation.
Step-by-step explanation:
To find the equation of a line that is perpendicular to x + 3y = -3 and passes through the point (4,2), we need to determine the slope of the given line and then use that slope to find the slope of the perpendicular line.
The given line can be written in slope-intercept form as y = (-1/3)x - 1. The slope of this line is -1/3.
Since perpendicular lines have slopes that are negative reciprocals of each other, the slope of the perpendicular line is 3.
Using the point-slope form of a linear equation, we can write the equation of the perpendicular line as y - 2 = 3(x - 4). Simplifying this equation gives the slope-intercept form y = 3x - 10.