Question

Determine whether each function is increasing, decreasing, or constant, and explain each one.

Y = (1/2)x + 5
2x + 4y = 12
Y = -3x - 7
3x + 5y = 15
(x + 2/6) + 2y = 2y
(-2x + 3/5) = 3y

Answer 1

The function (1/2)x + 5 is increasing, 2x + 4y = 12 is decreasing, Y = -3x - 7 is decreasing, and 3x + 5y = 15 is constant.

Step-by-step explanation:

The function y = (1/2)x + 5 is increasing. It has a positive slope of 1/2, which means that as the value of x increases, the corresponding value of y also increases. The function starts with a y-intercept at 5, then the values of y increase as x increases.

The function 2x + 4y = 12 is decreasing. It can be rewritten as y = (-1/2)x + 3, which has a negative slope of -1/2. As x increases, the corresponding values of y decrease, resulting in a downward slope.

The function Y = -3x - 7 is also decreasing. It has a negative slope of -3, which means that as x increases, the values of y decrease. The function starts with a y-intercept at -7, then the values of y decrease as x increases.

The function 3x + 5y = 15 is constant. It can be rewritten as y = (-3/5)x + 3, which has a slope of -3/5. However, the coefficient of y is positive, which means that as the value of x increases, the corresponding values of y remain the same.