The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m = slope
c = y intercept
The given equations are
y - x = 3
x + y = -5
We would make both equations to look like the slope intercept equation. We have
For y - x = 3,
Adding x to both sides of the equation, we have
y - x + x = 3 + x
y = x + 3
The slope is 1
For x + y = - 5,
Subtracting x from both sides of the equation, we have
x - x + y = - 5 - x
y = - x - 5
The slope is - 1
Recall, if two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line. We know that 1 is the - 1
Thus, the lines are perpendicular
