Question

Find the equation of the line with the given properties. Sketch the graph of the line. Passes through (1, -6) and (8,3)

Answer 1

A line equation can be written in slope-intercept form, which is

`y=mx+b`

Where m represents the slope and b the y-intercept.

If we evaluate our points on this form, we're going to have a linear system where the solutions are those coefficients.

`\begin{cases}3=8m+b \\ -6=m+b\end{cases}`

If we subtract the second equation from the first, we're going to have a new equation only for the slope.

`\begin{gathered} 3-(-6)=8m+b-(m+b) \\ 3+6=8m+b-m-b \\ 9=7m \\ m=(9)/(7) \end{gathered}`

Now that we have the slope, we can use any of the equations to find the b value.

`\begin{gathered} -6=((9)/(7))+b \\ -6-(9)/(7)=b \\ b=-(51)/(7) \end{gathered}`

Then, our line equation is

`y=(9)/(7)x-(51)/(7)`

And this is the graph