Question

If a line passes through (-4,3) and (6,2) what's the equation if an equation isn't possible say no

Answer 1

First, let's find the slope of the line that passes through the points (-4,3) and (6,2):

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ \Rightarrow m=(2-3)/(6-(-4))=(-1)/(6+4)=-(1)/(10) \end{gathered}`

Now we can use the first point to get the equation of the line:

`\begin{gathered} (x_1,y_1)=(-4,3) \\ y-y_1=m(x-x_1) \\ \Rightarrow y-3=-(1)/(10)(x-(-4))=-(1)/(10)(x+4)=-(1)/(10)x-(4)/(10)=-(1)/(10)x-(2)/(5) \\ \Rightarrow y=-(1)/(10)x-(2)/(5)+3=-(1)/(10)x-(2)/(5)+(15)/(5)=-(1)/(10)x+(13)/(5) \\ y=-(1)/(10)x+(13)/(5) \end{gathered}`

therefore, the equation of the line is y=-1/10x+13/5