a)
The slope intercept equation of a line is expressed as
y = mx + c
where
m is the slope
c is the y intercept
The given equation is
x + y = 3
y = - x + 3
By comparing both equations,
m = - 1
If two equations are parallel, it means that they have the same slope. Thus, the slope of the parallel line passing through the point (- 3, 2) is - 1
We would find the y intercept by substituting x = - 3, y = 2 and m = - 1 into the slope intercept equation. It becomes
2 = - 1 * - 3 + c
2 = 3 + c
c = 2 - 3
c = - 1
By substituting m = - 1 and c = - 1 into the slope intercept equation, the equation of the line is
y = - x - 1
b) If two equations are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line Thus, the slope of the perpendicular line passing through the point (- 3, 2) is - - 1/1 = 1
We would find the y intercept by substituting x = - 3, y = 2 and m = 1 into the slope intercept equation. It becomes
2 = 1 * - 3 + c
2 = - 3 + c
c = 2 + 5
c = 5
By substituting m = 1 and c = 5 into the slope intercept equation, the equation of the line is
y = x + 5
a) y = - x - 1
b) y = x + 5