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: [tex]y=mx+b[/tex], where m is the slope and b is the y-intercept.
To find the slope, you must use the following equation:
[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
In this equation, this would be equivalent to:[tex]\frac{-6-(-5)}{-7-(-1)}[/tex] which, when simplified, is [tex]\frac{1}{6}[/tex]. 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 [tex]\frac{1}{6}[/tex] for the m term.
[tex]-6 = (\frac{1}{6})(-7) + b[/tex] leads to [tex]-6 = \frac{-7}{6} +b[/tex] which leads to [tex]\frac{-29}{6} = b[/tex]. You have now solved for the y-intercept and aare ready to form your final equation.
The final equation is:[tex]y=\frac{1}{6}x -\frac{29}{6}[/tex]
