Answer:
The slope of f(x) is 4 and y-intercept is -3. It is an decreasing function.
The slope of g(x) is -4 and y-intercept is -3. It is an decreasing function.
The slope of h(x) is -4 and y-intercept is 3. It is an increasing function.
The slope of j(x) is 4 and y-intercept is 3. It is an increasing function.
Step-by-step explanation:
The slope intercept form of a line is
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
Where, m is slope and b is y-intercept.
If a line passing though two points, then the equation of line is
![y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%28x-x_1%29)
From the given information it is noticed that the function f(x) passing through the points (1,1) and (2,5).
![y-1=\frac{5-1}{2-1}(x-1)](https://tex.z-dn.net/?f=y-1%3D%5Cfrac%7B5-1%7D%7B2-1%7D%28x-1%29)
![y=4x-4+1](https://tex.z-dn.net/?f=y%3D4x-4%2B1)
![f(x)=4x-3](https://tex.z-dn.net/?f=f%28x%29%3D4x-3)
The slope of f(x) is 4 and y-intercept is -3. It is an decreasing function.
From the given information it is noticed that the function g(x) passing through the points (0,-3) and (-2,5).
![y+3=\frac{5+3}{-2-0}(x-0)](https://tex.z-dn.net/?f=y%2B3%3D%5Cfrac%7B5%2B3%7D%7B-2-0%7D%28x-0%29)
![g(x)=-4x-3](https://tex.z-dn.net/?f=g%28x%29%3D-4x-3)
The slope of g(x) is -4 and y-intercept is -3. It is an decreasing function.
The function h(x) is
![h(x)=-4x+3](https://tex.z-dn.net/?f=h%28x%29%3D-4x%2B3)
The slope of h(x) is -4 and y-intercept is 3. It is an increasing function.
It is given the initial amount of hat is 3 and number of hats increased by 4. So the function j(x).
![f(x)=4x+3](https://tex.z-dn.net/?f=f%28x%29%3D4x%2B3)
The slope of j(x) is 4 and y-intercept is 3. It is an increasing function.