Respuesta :
The point-slope equation is the following:
[tex]y-y_1=m(x-x_1)[/tex]Where (x1, y1) is a point of the line and m is the slope.
The slope is calculated as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where (x1, y1) and (x2, y2) are points of the line. So, replacing (x1, y1) by (-2, 6) and (x2, y2) by (5, 1), we get:
[tex]m=\frac{1-6}{5-(-2)}=\frac{-5}{5+2}=\frac{-5}{7}[/tex]Then, the point-slope form is:
[tex]\begin{gathered} y-6=\frac{-5}{7}(x-(-2)) \\ y-6=\frac{-5}{7}(x+2) \end{gathered}[/tex]Finally, to rewrite the equation in slope-intercept form, we need to solve for y as:
[tex]\begin{gathered} y-6=\frac{-5}{7}(x+2) \\ y-6=\frac{-5}{7}x+\frac{-5\cdot2}{7} \\ y-6=\frac{-5x}{7}-\frac{10}{7} \\ y=\frac{-5x}{7}-\frac{10}{7}+6 \\ y=\frac{-5x}{7}+\frac{32}{7} \end{gathered}[/tex]Answer: Point-slope form:
[tex]y-6=\frac{-5}{7}(x+2)[/tex]Slope-Intercept form:
[tex]y=\frac{-5}{7}x+\frac{32}{7}[/tex]