Final answer:
The student is looking to find the slope of a line perpendicular to two given lines and to write the equation of that line in point-slope form through specific points. The perpendicular slope is -3/2, and the point-slope form of the equation through point A(-2,5) is y - 5 = -3/2(x + 2).
Step-by-step explanation:
The student is asking about the slope of a line that would be perpendicular to another and how to write the point-slope form of the equation for that line through given points.
To find the slope of the line that is perpendicular to both given lines, we recall that perpendicular lines have opposite reciprocal slopes.
Given that the first line has a slope of 2/3, the slope of the line perpendicular to both lines would be -3/2.
With this, and using the first given point A(-2,5), we can write the point-slope form of the third line as y - y1 = m(x - x1), where m is the slope and (x1, y1) is point A.
So the equation is y - 5 = -3/2(x + 2).
Using the given line graphs and the algebra of straight lines, we understand that the slope 'm' and the y-intercept 'b' uniquely determine the shape and position of a linear graph on the Cartesian plane.