The way that you find this problem is to first find the slope, and then input one of your points into your equation to find b.
The slope-intercept form of a line is: \(y=mx+b\), where m is the slope and b is the y-intercept.
To find the slope, you must use the following equation:
\(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)
In this equation, this would be equivalent to:\(\frac{-6-(-5)}{-7-(-1)}\) which, when simplified, is \(\frac{1}{6}\). This is your slope.
To find the Y-intercept, you just plug all variables that you currently have solved for into the equation. You may use either point for the x and y variables, but you must use \(\frac{1}{6}\) for the m term.
\(-6 = (\frac{1}{6})(-7) + b\) leads to \(-6 = \frac{-7}{6} +b\) which leads to \(\frac{-29}{6} = b\). You have now solved for the y-intercept and aare ready to form your final equation.
The final equation is:\(y=\frac{1}{6}x -\frac{29}{6}\)
