The slope of a line is calculated using the formula:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]For the points (-6, 7) and (-3, 6)
[tex]\begin{gathered} x_1=-6,y_1=7,x_2=-3,y_2=6 \\ m\text{ = }\frac{6-7}{-3-(-6)} \\ m\text{ = }\frac{-1}{3} \end{gathered}[/tex]The slope = -1/3
The point-slope form of the equation of a line is:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y\text{ - 7 = }\frac{-1}{3}(x\text{ - (-6))} \\ y\text{ - 7 = }\frac{-1}{3}(x\text{ + 6)} \end{gathered}[/tex]To find the slope-intercept form, reduce the equation above to the form:
y = mx + c
[tex]\begin{gathered} y\text{ - 7 = }\frac{-1}{3}(x\text{ + 6)} \\ y\text{ - 7 = }\frac{-1}{3}x\text{ - 2} \\ y\text{ = }\frac{-1}{3}x\text{ - 2 + 7} \\ y\text{ = }\frac{-1}{3}x\text{ + 5} \end{gathered}[/tex]