To find the slope of a line parallel to a given line, we need to find the slope of the given line and use it as the slope of the new line. The slope of a line can be found by using the formula slope = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.
To find the slope of a line parallel to the line y=-x-5, we can use the formula to find the slope of the given line. We can choose any two points on the line to use in the formula, but it is often convenient to choose two points that are easy to work with. In this case, we can choose the points (1, -1-5) and (2, -2-5) as the points to use in the formula. Plugging these values into the formula, we get slope = (-1-5 - (-2-5))/(1 - 2) = (-6 - (-7))/(-1) = 1.
Therefore, the slope of a line parallel to y=-x-5 is 1.
To find the slope of a line parallel to the line y=2x-2, we can use the formula to find the slope of the given line. We can choose any two points on the line to use in the formula, but it is often convenient to choose two points that are easy to work with. In this case, we can choose the points (1, 21-2) and (2, 22-2) as the points to use in the formula. Plugging these values into the formula, we get slope = (21-2 - 22-2)/(1 - 2) = (0 - (-2))/(-1) = 2.
Therefore, the slope of a line parallel to y=2x-2 is 2.
To find the slope of a line perpendicular to a given line, we need to find the slope of the given line and use the negative reciprocal of the slope as the slope of the new line. The negative reciprocal of a slope is calculated by taking the reciprocal of the slope (which is the inverse of the slope), and then negating the result. For example, the negative reciprocal of a slope of 2 is -1/2, and the negative reciprocal of a slope of -3 is 1/3.
To find the slope of a line perpendicular to the line y=-x-1, we can first use the formula to find the slope of the given line. We can choose any two points on the line to use in the formula, but it is often convenient to choose two points that are easy to work with. In this case, we can choose the points (1, -1-1) and (2, -2-1) as the points to use in the formula. Plugging these values into the formula, we get slope = (-1-1 - (-2-1))/(1 - 2) = (-2 - (-3))/(-1) = 1.
Therefore, the slope of the given line is 1. To find the slope of a line perpendicular to this line,