Answer:
![y=2x](https://tex.z-dn.net/?f=y%3D2x)
Step-by-step explanation:
We want to write an equation in slope-intercept form that passes through the points (2, 4) and (3, 6).
So, we will first find the slope. Let (2, 4) be (x₁, y₁) an let (3, 6) be (x₂, y₂).
The slope formula is given by:
![\displaystyle m=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
So, by substitution, our slope is:
![\displaystyle m=\frac{6-4}{3-2}=\frac{2}{1}=2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20m%3D%5Cfrac%7B6-4%7D%7B3-2%7D%3D%5Cfrac%7B2%7D%7B1%7D%3D2)
Now, we can use the point-slope form:
![y-y_1=m(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29)
By substitution:
![y-(4)=2(x-(2))](https://tex.z-dn.net/?f=y-%284%29%3D2%28x-%282%29%29)
Distribute:
![y-4=2x-4](https://tex.z-dn.net/?f=y-4%3D2x-4)
Adding 4 to both sides yields:
![y=2x](https://tex.z-dn.net/?f=y%3D2x)
And we have our equation.
In this case, the y-intercept is 0.