Final answer:
To find the equation of a line perpendicular to 3x - 5y = 1 and passing through the point (9, -9), we rearrange the given equation to slope-intercept form, find the negative reciprocal of the slope, and then use the point-slope form of a line.
Step-by-step explanation:
To find the equation of a line perpendicular to the given line, we need to find its slope and then use the point-slope form of a line. The given line has the equation 3x - 5y = 1, so we need to rearrange it to slope-intercept form by solving for y:
-5y = -3x + 1
y = (3/5)x - 1/5
The slope of the given line is 3/5. The slope of a line perpendicular to it will be the negative reciprocal of this slope, which is -5/3. Since we know the line passes through the point (9, -9), we can use the point-slope form to find its equation:
y - y1 = m(x - x1)
y - (-9) = -5/3(x - 9)
y + 9 = -5/3(x - 9)
y + 9 = -5/3x + 15
y = -5/3x + 15 - 9
The equation of the line that passes through the point (9, -9) and is perpendicular to 3x - 5y = 1 is y = -5/3x + 6.