Based on the slope, the lines are related as option (2) they are perpendicular is the correct answer.
What is slope of a line?
The slope or gradient of a line is a number that describes both the direction X and Y and the steepness of the line. It is the ratio of the vertical change to the horizontal change between any two distinct points on a line.
For the given situation,
The lines are x+y=2 and y=x+4.
The diagram below shows the graph of the line 1 and line 2 that are perpendicular to each other.
The equation of line in slope intercept form is
[tex]y=mx+c[/tex] -------- (1)
Now consider the line 1,
[tex]x+y=2[/tex]
⇒ [tex]y=-x+2[/tex] -------- (2)
on comparing line 1 with equation 1,
Here, the slope [tex]m1 = -1[/tex].
Now consider the line 2,
[tex]y=x+4[/tex]
on comparing line 2 with equation 1,
Here, the slope [tex]m2=1[/tex] -------- (3)
Thus the slope of line 1 is the negative reciprocal of line 2,
⇒ [tex]m1=\frac{-1}{m2}[/tex]
Hence we can conclude that the based on the slope, the lines are related as option (2) they are perpendicular is the correct answer.
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