Answer:
A. ![y =\frac{7}{8}x+1](https://tex.z-dn.net/?f=y%20%3D%5Cfrac%7B7%7D%7B8%7Dx%2B1)
B. ![y = -10x](https://tex.z-dn.net/?f=y%20%3D%20-10x)
C. ![y = 2.5x - 7](https://tex.z-dn.net/?f=y%20%3D%202.5x%20-%207)
D. ![y = 1.2x](https://tex.z-dn.net/?f=y%20%3D%201.2x)
E. ![y = -5x -8](https://tex.z-dn.net/?f=y%20%3D%20-5x%20-8)
Step-by-step explanation:
Let the descriptions be A to E.
First, we need to note the followings.
An equation is of the form
and ![b = y\ intercept](https://tex.z-dn.net/?f=b%20%3D%20y%5C%20intercept)
A. Non proportional graph with positive y intercept
From the list of options, only
The slope of
is positive
and y intercept is also positive
B. Negative slope and pass through the origin.
Negative slope means m is negative
From the list of options
and ![y = -5x -8](https://tex.z-dn.net/?f=y%20%3D%20-5x%20-8)
Origin implies (0,0)
i.e:
and ![y = 0](https://tex.z-dn.net/?f=y%20%3D%200)
For y = -10x
![0 = -10 * 0](https://tex.z-dn.net/?f=0%20%3D%20-10%20%2A%200)
--- This is true
For ![y = -5x -8](https://tex.z-dn.net/?f=y%20%3D%20-5x%20-8)
![0 = -5 * 0 - 8](https://tex.z-dn.net/?f=0%20%3D%20-5%20%2A%200%20-%208)
![0 = 0 - 8](https://tex.z-dn.net/?f=0%20%3D%200%20-%208)
--- This is not true
Hence:
fits this description
C. Increases from left to right and b is negative
For b is negative, we have the following:
and
![y = 2.5x - 7](https://tex.z-dn.net/?f=y%20%3D%202.5x%20-%207)
An increment from left to right, means the slope is positive.
So, we have:
![y = 2.5x - 7](https://tex.z-dn.net/?f=y%20%3D%202.5x%20-%207)
D. Positive slope and contains (0,0)
From the options, we have the following functions left:
and
![y = 1.2x](https://tex.z-dn.net/?f=y%20%3D%201.2x)
But
has a positive slope and also contain (0,0) because
![0 = 1.2 * 0](https://tex.z-dn.net/?f=0%20%3D%201.2%20%2A%200)
![0 = 0](https://tex.z-dn.net/?f=0%20%3D%200)
E. Negative m and Negative b
has these descriptions