Final answer:
The equation of the line that passes through the point (4, -3) and is perpendicular to 2x - 5y = 35 is y = (-5/2)x + 7.
Step-by-step explanation:
To find the equation of a line that is perpendicular to another line, we first need to determine the slope of the given line. The given line has an equation 2x - 5y = 35. We can rearrange this equation in slope-intercept form (y = mx + b) by solving for y:
2x - 5y = 35
-5y = -2x + 35
y = (2/5)x - 7
The slope of the given line is 2/5. The slope of a line that is perpendicular to another line is the negative reciprocal of the slope of the given line. So the slope of the perpendicular line is -5/2.
We also have a point that the perpendicular line passes through, which is (4, -3). Using the slope-intercept form of a line (y = mx + b), we can substitute the known values to find b:
-3 = (-5/2)(4) + b
-3 = -10 + b
b = 7
Therefore, the equation of the line that passes through the point (4, -3) and is perpendicular to 2x - 5y = 35 is y = (-5/2)x + 7.