Final answer:
To find the equation of a line that passes through a given point and intersects another line to form a right angle, we need to determine the slope of the given line and then find the negative reciprocal of that slope. Using the point-slope form of a linear equation, we can write the equation of the perpendicular line.
Step-by-step explanation:
To find the equation of the line that passes through (-2, 4) and intersects the line 2x + 5y = 7 to form a right angle, we need to determine the slope of the given line and then find the negative reciprocal of that slope. The given line has the equation 2x + 5y = 7, which can be rewritten as y = (-2/5)x + 7/5. The slope of this line is -2/5, so the slope of the line perpendicular to it is 5/2.
Using the point-slope form of a linear equation, we can write the equation of the perpendicular line as y - 4 = (5/2)(x + 2). Simplifying this equation, we get y = (5/2)x + 9.