Answer:
To find the equation of a line that is perpendicular to the line y = x - 4 and goes through the origin (0,0), we can use the slope-intercept form of a line, which is y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).
The slope of a line is defined as the change in y divided by the change in x between two points on the line. The slope of the line y = x - 4 is 1, since the line has a slope of 1. A line that is perpendicular to this line must have a slope that is the negative reciprocal of 1, which is -1.
So, the equation of the line that is perpendicular to y = x - 4 and goes through the origin is y = -x.
Note that the y-intercept is 0, since the line goes through the origin.
Explanation: