Final answer:
To find the equation of a line perpendicular to x−3y=3 and passing through the point (5, -9), use the negative reciprocal of the slope of the given line. The equation of the perpendicular line is y = 3x - 6.
Step-by-step explanation:
To find the equation of a line that is perpendicular to the line x−3y=3 and passes through the point (5, -9), we need to find the slope of the given line and then use the negative reciprocal of that slope to find the slope of the perpendicular line. The given line has the slope -1/3, so the slope of the perpendicular line is 3/1. Using the point-slope form of a line, we can write the equation of the perpendicular line as:
y - y1 = m(x - x1)
Substituting the values of the point (5, -9) and the slope 3/1 into the equation, we get:
y - (-9) = (3/1)(x - 5)
Simplifying the equation gives us:
y + 9 = 3x - 15
Finally, rearranging the equation to the slope-intercept form gives us:
y = 3x - 15 - 9
which simplifies to:
y = 3x - 6