Answer:
To find the equation of a line that is perpendicular to another line and passes through a given point, we can use the slope-point form of the line equation.
The first step is to find the slope of the given line. To do this, we can rearrange the equation 5x - 3y = 2 into slope-intercept form:
y = (5/3)x + 2/3
So the slope of the given line is 5/3.
Next, we need to find the slope of the line that is perpendicular to this line. The slope of a perpendicular line is the negative reciprocal of the original line's slope.
The negative reciprocal of 5/3 is -3/5.
Now that we have the slope, we can use the point-slope form of a line to find the equation of the line that is perpendicular to 5x - 3y = 2 and passes through the point (-1/4, 3/5):
y - 3/5 = -3/5 (x + 1/4)
Expanding the right side:
y - 3/5 = -3/5x - 3/20
Adding 3/5 to both sides:
y = -3/5x + 3/4
So the equation of the line that is perpendicular to 5x - 3y = 2 and passes through the point (-1/4, 3/5) is y = -3/5x + 3/4.