The equation of the line in slope - intercept form is ![y=-3x+1](https://tex.z-dn.net/?f=y%3D-3x%2B1)
Explanation:
From the graph, the given coordinates are
and ![(1,-4)](https://tex.z-dn.net/?f=%281%2C-4%29)
We need to determine the equation of the line in slope intercept form.
The equation of the line can be determined using the formula,
![y-y_1=m(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29)
First, we shall find the value of the slope.
The slope can be determined by substituting the points
and
in the slope formula, we get,
![m=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
![m=\frac{-4-2}{1+1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-4-2%7D%7B1%2B1%7D)
![m=\frac{-6}{2}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-6%7D%7B2%7D)
![m=-3](https://tex.z-dn.net/?f=m%3D-3)
Thus, the slope is ![m=-3](https://tex.z-dn.net/?f=m%3D-3)
Now, we shall substitute the coordinate
and the slope
in the formula
, we get,
![y-2=-3(x+1)](https://tex.z-dn.net/?f=y-2%3D-3%28x%2B1%29)
![y-2=-3x-3](https://tex.z-dn.net/?f=y-2%3D-3x-3)
![y=-3x+1](https://tex.z-dn.net/?f=y%3D-3x%2B1)
Thus, the equation of the line in slope intercept form is ![y=-3x+1](https://tex.z-dn.net/?f=y%3D-3x%2B1)