To find the coordinates of a point B so that the line segment AB has a specific slope, you can use the formula for calculating the slope of a line, which is (y2 - y1) / (x2 - x1). Given the point A(-2, 5) and the desired slopes, we can proceed as follows:
a) Slope = 23:
Let the coordinates of point B be (x, y). Using the formula for slope, (y - 5) / (x - (-2)) = 23. Solve for x and y to find the coordinates of point B.
b) Slope = 3:
Repeat the process as in part (a), but this time set the slope equal to 3 and solve for the coordinates of point B.
c) Slope = 4:
Similarly, set the slope to 4 and find the coordinates of point B using the formula for slope and the given point A(-2, 5).
d) Slope = -3:
Follow the steps outlined in parts (a) and (b), but this time set the slope to -3 and solve for the coordinates of point B.
e) Slope = 0:
For a slope of 0, the line is horizontal. Therefore, the y-coordinate of point B should be the same as the y-coordinate of point A(-2, 5). You can find the x-coordinate of point B accordingly.
f) Slope = undefined:
An undefined slope corresponds to a vertical line. In this case, the x-coordinate of point B should be the same as the x-coordinate of point A(-2, 5). Determine the y-coordinate of point B accordingly.
By following these steps and using the formula for slope, you can calculate the coordinates of point B for each given slope.
