Answer:
Step-by-step explanation:
We will define the functions as:
f(x)=5+2x from the given information:
Now we have three points: (-2,-9) ,(-1,6) and (2,-17)
We will use two point form to find g(x)
![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)
We will use the point (-2,-9) and (-1,6) on substituting the values in the above formula we get:
![y-(-9)=\frac{6+9}{-1+2}(x+2)](https://tex.z-dn.net/?f=y-%28-9%29%3D%5Cfrac%7B6%2B9%7D%7B-1%2B2%7D%28x%2B2%29)
On simplification we get:
![y=-15x-39](https://tex.z-dn.net/?f=y%3D-15x-39)
![g(x)=-15x-39](https://tex.z-dn.net/?f=g%28x%29%3D-15x-39)
Now, we will form h(x) from the points (0,5) and (3,-1) with the two point form:
![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)
![y-5=\frac{-1-5}{3-0}(x-0)](https://tex.z-dn.net/?f=y-5%3D%5Cfrac%7B-1-5%7D%7B3-0%7D%28x-0%29)
On simplification we will get:
![y=-2x+5](https://tex.z-dn.net/?f=y%3D-2x%2B5)
![h(x)=-2x+5](https://tex.z-dn.net/?f=h%28x%29%3D-2x%2B5)
Now, we have j(x)=2x-5
We will compare the function with general equation y= mx+c; m is slope of line.
And to find y-intercept put x =0 in the given function.
The slope of f(x)=5+2x is 2 because 2 is coefficient of x which is m
And y-intercept is: (0,5).
g(x)=-15x-39
Slope of g(x) is -15
And y-intercept is: (0,-39).
h(x)=-2x+5
Slope of h(x) is: -2
And y-intercept is: (0,5)
j(x)=2x-5
Slope of j(x) is: 2
And y-intercept is: (0,-5).