Question

Consider the line y = x+ 4.What is the slope of a line parallel to this line?What is the slope of a line perpendicular to this line?Slope of a parallel line:Slope of a perpendicular line:

Answer 1

Given:

`y=x+4`

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,

`m=-(1)/(1)=-1`

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