Answer:
Step-by-step explanation:
A linear function has been given as,
y = ![\frac{1}{3}x+5](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7Dx%2B5)
Comparing it with the slope intercept equation,
y = mx + b
b = y-intercept = 5
From the graph,
y-intercept = (-2)
From the given table,
For x = 0, f(x) = 3
Therefore, y-intercept = 3
A line passes through two points (-3, -2) and (3, 0),
Slope of the line = ![\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
= ![\frac{0+2}{3+3}](https://tex.z-dn.net/?f=%5Cfrac%7B0%2B2%7D%7B3%2B3%7D)
= ![\frac{1}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D)
Equation of a line passing through a point (x', y') and slope = m
y - y' = m(x - x')
If the point is (3, 0) and slope = ![\frac{1}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D)
y - 0 = ![\frac{1}{3}(x-3)](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%28x-3%29)
y = ![\frac{1}{3}x-1](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7Dx-1)
y-intercept of this line = (-1)
Therefore, decreasing order of the slopes will be,
![5>3>\frac{1}{3}>(-2)](https://tex.z-dn.net/?f=5%3E3%3E%5Cfrac%7B1%7D%7B3%7D%3E%28-2%29)
Order of the functions with slopes from maximum to lease will be,
1).
2). Function represented by the table.
3). Line passing through (-3, -2) and (3, 0)
4). Function shown in the graph