Final answer:
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 can use the point-slope form of a line. The equation of the line is y = -1/2x + 1.
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 first need to determine the slope of the given line. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. In this case, the given line 2x + 5 = 7 can be rewritten as y = 2x - 2. Since two lines are perpendicular if their slopes are negative reciprocals of each other, the slope of the line we are trying to find is -1/2.
Using the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope, we can substitute the values (-2, 4) and -1/2 into the equation:
y - 4 = -1/2(x - (-2))
Simplifying the equation gives us:
y - 4 = -1/2(x + 2)
Now, we can rewrite the equation in slope-intercept form:
y = -1/2x + 1