Given:
Required: Slopes of parallel and perpendicular lines to y = x+4
First, find the slope of the line y = x+4. The given equation of line is in the form y = mx+c, where m is the slope and c is the y-intercept.
Comparing y = x+4 with y = mx+c gives m = 1 and c =4. So, the slope of the given line is 1.
Slopes of parallel lines are same. Hence the slope of a line parallel to y = x+4 is 1.
If two lines are perpendicular, the slopes are negative reciprocals.
Let 'm' be the slope of the line perpendicular to the line y = x+4. Then 'm' is the negative reciprocal of the slope of the line y = x+4, that is,
Hence the slope of the line perpendicular to the line y = x+4 is -1.
Final Answer:
Slope of a parallel line = 1
Slope of a perpendicular line = -1