determine if the following functions are increasing or decreasing and compare their rates of change 1) y=-x-3
2)a line which passes through the points (3,1) and (4,-2)
1) The function y = -x - 3 is a linear function with a negative slope (-1). Since the coefficient of x is negative, the function is decreasing. The rate of change is constant and equal to -1.
2) To find the equation of the line passing through the points (3, 1) and (4, -2), we can use the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
First, find the slope (m):
m = (change in y) / (change in x)
m = (-2 - 1) / (4 - 3)
m = -3 / 1
m = -3
Now substitute one of the points into the equation y = mx + b to find the y-intercept:
1 = -3(3) + b
1 = -9 + b
b = 10
So, the equation of the line passing through the points (3, 1) and (4, -2) is y = -3x + 10.
Since the coefficient of x is -3, the function is decreasing. The rate of change is also constant and equal to -3.