f (x ) = 2 x + 5 For g (x) we will solve the system: - 1 =-2 m + b + -9 = 2 m + b ---------------------- -10 = 2 b, b = -5 -9 = 2 m - 5 2 m = -4 m = -2 g ( x ) = - 2 x - 5 For h (X): m = (-1-5 ) / ( 3-0 ) = -6/3 = -2 5 = 0 + b, b = 5 h ( x) = - 2 x + 5. Now we have 4 linear functions: 1 ) f ( x ) = 2 x + 5 The slope is m = 2, y - intercept: y = 5 , zero: x = -2.5 and the function increases ( m > 0 ). 2 ) g(x) = - 2 x - 5 The slope is m = - 2, y-intercept: y =-5 , zero: x = -2.5 and the function decreases ( m < 0 ). 3 ) h ( x ) = - 2 x + 5 The slope is m = - 2, y - intercept . y = 5, zero: x = 2.5 and the function decreases. 4 ) j (x) = 2 x + 5 The slope is m = 2, y -intercept: y = 5, zero: x = -2.5 and the function decreases. The functions f( x ) and j ( x ) are parallel and also g( x ) and h ( x ). They have the same slope. The functions f ( x ) and j (x ) are increasing and h ( x ) and h ( x ) are decreasing.
