15. the equation of a line is x + y = 3
a) write the equation of the line that passes through the point (3,-8) and is parallel to the given
line.
b) write the equation of the line that passes through the point (4,-1) and is perpendicular to the
given line.

a) equation: y = mx + b        y = - x -5

b) equation: y = x - 5

Step-by-step explanation:

x + y = 3   i.e. y = - x + 3

slope(m) = - 1

a) parallel line: slope (m') = -1

pass (3 , - 8)   y intercept (b) = y - mx = -8 - (-1)x3 = -8 + 3 = -5

equation: y = mx + b        y = - x -5

b) perpendicular line slope = - 1/m = 1

pass (4 , - 1)   y intercept (b) = - 1 - (1 x 4) = - 5

equation: y = x - 5