Final answer:
The equation of the line that passes through (-5, -3) and is perpendicular to 5x - 3y = 18 is y = -3/5x - 6.
Step-by-step explanation:
To find the equation of a line that is perpendicular to another line, we need to find the negative reciprocal of the slope of the given line.
First, let's find the slope of the given line. Rewrite the equation in slope-intercept form (y = mx + b):
5x - 3y = 18
-3y = -5x + 18
y = (5/3)x - 6
So, the slope of the given line is 5/3.
The slope of the line perpendicular to the given line is the negative reciprocal of 5/3, which is -3/5.
Now we have the slope (-3/5) and the point (-5, -3) that the line passes through. We can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
where (x1, y1) is the point and m is the slope.
So the equation of the line that passes through (-5, -3) and is perpendicular to 5x - 3y = 18 is:
y - (-3) = -3/5(x - (-5))
y + 3 = -3/5(x + 5)
y + 3 = -3/5x - 3
y = -3/5x - 6