Question

What is an equation of the line that passes through the points (4, -1) and (8,5)? Put your answer in fully reduced form.

Answer 1

The equation of the line that passes thought the a point (x1,y1) and has slope m is

`y-y_1=m(x_{}-x_1)`

In our case we have two point but we don't know the slope yet. The slope is given by

`m=(y_2-y_1)/(x_2-x_1)`

Then, in our problem, the slope is

`\begin{gathered} m=(5-(-1))/(8-4) \\ =(5+1)/(4) \\ =(6)/(4) \\ =(3)/(2) \end{gathered}`

Once we have the slope and the point (we can use whichever we like) we can write the equation of the line; using the point (4,-1) we have:

`\begin{gathered} y-(-1)=(3)/(2)(x-4) \\ y+1=(3)/(2)x-(12)/(2) \\ y+1=(3)/(2)x-6 \\ y=(3)/(2)x-6-1 \\ y=(3)/(2)x-7 \end{gathered}`