Final answer:
To find a parallel line, use the same slope as the given line with a different y-intercept. The slope determines the line's angle, while the y-intercept is where it crosses the y-axis. The correct answer is option a).
Step-by-step explanation:
To find a line that is parallel to another line, you would use the same slope as the given line but a different y-intercept. This is because parallel lines have the same steepness or inclination but do not necessarily cross the y-axis at the same point. From the slope and y-intercept of a linear equation, such as y = a + bx, we understand that b represents the slope and a represents the y-intercept. In the context of the question, the correct answer would be option a) Use the same slope as the given line but a different y-intercept.
In Figure A1, we see a line with a slope of 3. This means for every increase of 1 on the horizontal axis (x), there is a rise of 3 on the vertical axis (y). This slope remains the same all along a straight line. To illustrate with an equation: if the original line has the equation y = 9 + 3x, any parallel line will have the equation y = c + 3x, where c is any y-intercept value other than 9.