Final answer:
The equation of the line that passes through (-2, 4) and intersects the line 2x + 5 = 7 to form a right angle is y = -1/2x + 3.
Step-by-step explanation:
To find the equation of the line that passes through (-2, 4) and intersects the line 2x + 5 = 7 to form a right angle, we need to determine the slope of the given line and then find the perpendicular slope. The equation 2x + 5 = 7 can be simplified to 2x = 2, which gives us x = 1. Therefore, the line has a slope of 2. Since the line we want to find forms a right angle with this line, the perpendicular slope will be the negative reciprocal of 2, which is -1/2.
Using the given point (-2, 4) and the slope -1/2, we can substitute these values into the point-slope form of a linear equation, which is y - y1 = m(x - x1). Thus, the equation of the line is y - 4 = -1/2(x - (-2)). Simplifying this equation gives us y - 4 = -1/2(x + 2), or y - 4 = -1/2x - 1. Finally, we can rearrange the equation to the standard form, y = mx + b, where m is the slope and b is the y-intercept. Therefore, the equation of the line that passes through (-2, 4) and intersects the line 2x + 5 = 7 to form a right angle is y = -1/2x + 3.