Final answer:
To find the equation of the line perpendicular to the given line, we need to determine its slope and find the negative reciprocal of that slope. By rearranging the given equation into y = mx + b form, we find that the slope of the original line is -1. The negative reciprocal of -1 is 1, so the new line has a slope of 1. Since the new line passes through (0,0), we can use the point-slope form to find its equation, which is y = x. Correct option is B.
Step-by-step explanation:
To find the equation of a line perpendicular to another line, we need to determine the slope of the original line. The equation of the original line is x + y = -5. To find the slope, we need to rearrange the equation into y = mx + b form, where m represents the slope. So we have y = -x - 5. The slope of the original line is -1.
Since we want to find a line perpendicular to the original line, the slope of the new line will be the negative reciprocal of the original line's slope. The negative reciprocal of -1 is 1. So the new line has a slope of 1.
We also know that the new line passes through the point (0,0). Using the point-slope form, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line, we can substitute the known values into the equation. So we have y - 0 = 1(x - 0). Simplifying, we get y = x.
Therefore, the equation of the line perpendicular to x + y = -5, that passes through the point (0,0), and is written in slope-intercept form, is y = x. Therefore, the correct answer is B) y = x.