Answer:
[tex]\huge\boxed{1.\ y=-\frac{1}{2}x+1}[/tex]
[tex]\huge\boxed{2. \ y=\frac{3}{2}x}[/tex]
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 [tex]y=mx+b[/tex], where m is the slope and b is the y-intercept.
For number 1:
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. This is where the two dots come in useful. 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.
[tex]-1 \div 2 = -\frac{1}{2}[/tex]
Now that we know the slope and the y-intercept, we can plug these values into [tex]y=mx+b[/tex].
[tex]y=-\frac{1}{2}x+1[/tex]
For Number 2:
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 [tex]\frac{3}{2}[/tex].
[tex]y=mx+b[/tex]
[tex]y=\frac{3}{2}x[/tex]
Hope this helped!
