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

$m=\frac{y_2-y_1}{x_2-x_1}$

Then, in our problem, the slope is

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

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:

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