Answer:
![\huge\boxed{1.\ y=-\frac{1}{2}x+1}](https://tex.z-dn.net/?f=%5Chuge%5Cboxed%7B1.%5C%20%20y%3D-%5Cfrac%7B1%7D%7B2%7Dx%2B1%7D)
![\huge\boxed{2. \ y=\frac{3}{2}x}](https://tex.z-dn.net/?f=%5Chuge%5Cboxed%7B2.%20%5C%20y%3D%5Cfrac%7B3%7D%7B2%7Dx%7D)
Step-by-step explanation:
In order to find the equation for these graphs, we have to note what forms a line.
The slope: Which is just the rise of the line over the run - how much it increases in y over how much it increases in x.
The y-intercept: Where does the graph intersect the y-axis?
Fortunately, there's a type of formula commonly used that includes both of these - slope-intercept form. It is written in the form
, where m is the slope and b is the y-intercept.
<em>For number 1</em><em>:</em>
We can see that the graph intersects the y-axis at 1. So the y-intercept is 1, aka b = 1.
We can also see that for every 1 decrease in y, x increases by 2. <em>This is where the two dots come in useful</em>.<em> </em> This means our change in y is -1 and our change in x is 2. Since slope is rise over run, we can divide it.
![-1 \div 2 = -\frac{1}{2}](https://tex.z-dn.net/?f=-1%20%5Cdiv%202%20%3D%20-%5Cfrac%7B1%7D%7B2%7D)
Now that we know the slope and the y-intercept, we can plug these values into
.
![y=-\frac{1}{2}x+1](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B1%7D%7B2%7Dx%2B1)
<em>For Number 2:</em>
Same logic applies. The graph intersects the y-axis at 0, so b = 0, aka we don't need to include that term in the end equation.
We can see that when x increases by 2, y increases by 3. Since the slope is rise over run, the slope is
.
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
![y=\frac{3}{2}x](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B3%7D%7B2%7Dx)
Hope this helped!