Question

What is an equation of a line that passes through the points (3,4) and (4,6)

Answer 1

To find the equation of the line we must use the next equation

`y-y_1=m(x-x_1)`

First, we need to replace the two points to find the slope (m) of the line

`\begin{gathered} 6-4=m(4-3) \\ m=(6-4)/(4-3)=(2)/(1)=2 \end{gathered}`

Then, we must replace on the points and the slope in the initial equation

`\begin{gathered} y-6=2(x-4) \\ y-6=2x-8 \\ y-6-2x+8=0 \\ y-2x+2=0 \end{gathered}`

Finally, the equation of the line is

`y-2x+2=0`