Question

Find an equation for the line that passes through the point (6,1) and (-4,3)

Answer 1

We have to find the equation of the line.

We have two points that belong to the line: (6,1) and (-4,3).

We can start calculating the slope of the line as:

`m=(y_2-y_1)/(x_2-x_1)=(3-1)/(-4-6)=(2)/(-10)=-(1)/(5)`

We can now write the equation in slope-point form and rearrange:

`\begin{gathered} y-y_0=m(x-x_0) \\ y-1=-(1)/(5)(x-6) \\ y=-(1)/(5)x+(6)/(5)+1 \\ y=-(1)/(5)x+(6)/(5)+(5)/(5) \\ y=-(1)/(5)x+(11)/(5) \end{gathered}`

Answer: the equation of the line is y=-(1/5)*x+11/5