Final answer:
To reflect a figure through the horizontal axis, invert the y-coordinates; for reflecting through x = 0, change the x-coordinates' signs. For lines y = -x or x = -y, you would swap and change the signs of coordinates. The figure's line has a positive slope and rises upwards to the right as it moves to the right of the coordinate system.
Step-by-step explanation:
The student has asked to reflect a given figure through the horizontal axis and then through one of the listed lines. When reflecting a figure through the horizontal axis, also known as the x-axis, you invert the y-coordinates of the figure's points. The options 1) x = 0 and 2) y = 0 refer to the y-axis and x-axis, respectively, but given that the first reflection is across the x-axis, the only possible answers then are reflections across lines not parallel to it, which are 3) y = -x or 4) x = -y.
Upon reflection across the y-axis (x = 0), the signs of the x-coordinates of the points are changed. However, reflections across lines y = -x and x = -y involve more complex transformations that include swapping and changing signs of the coordinates.
The line in Figure A1 has a positive slope since there is a rise of 3 on the vertical axis for every increase of 1 on the horizontal axis. This means that the line goes vertically upward in the coordinate system as it moves horizontally to the right side of the coordinate system.
Given the provided information, we can determine that the straight line has a positive slope and has a y-intercept at 9, indicating the line starts at point (0,9) and rises up to the right. Therefore, answer option b (It is a straight line with positive slope) is the correct description based on the provided details of the slope and y-intercept.