Question

find an equation of the line passing through the pair of points. write an equation in the form Ax+By=C (3,1) and (5,7)

Answer 1

The two points given are:

$\begin{gathered} (x_1,y_1)=(3,1) \\ \text{and} \\ (x_2,y_2)=(5,7) \end{gathered}$

Let's find the slope, m, first:

$\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{7-1}{5-3} \\ m=\frac{6}{2} \\ m=3 \end{gathered}$

We can now use the point slope form of a line to figure out the equation. Process is shown below:

$\begin{gathered} y-y_1=m(x-x_1)_{} \\ y-1=3(x-3) \\ y-1=3x-9 \\ y=3x-9+1 \\ y=3x-8 \end{gathered}$

We re-arrange in the form Ax + By = C,

$\begin{gathered} y=3x-8 \\ -3x+y=-8 \end{gathered}$