Equation of a line can be given by :
y = mx + b
Let's find the slope of the line (m) :
[tex] \mathcal{ \hookrightarrow \: \dfrac{y_2 - y_1}{x_2 - x_1} }[/tex]
[tex] \mathcal{ \hookrightarrow \: \dfrac{ - 1 - ( - 7)}{0 - 5} }[/tex]
[tex] \hookrightarrow \: \dfrac{6}{ - 5} [/tex]
[tex] \hookrightarrow \: m = \dfrac{ - 6}{5} [/tex]
now let's solve for b :
[tex] \hookrightarrow \: y = mx + b[/tex]
Let's plug the values of x and y from the coordinates of a point .
[tex] \hookrightarrow \: - 7 = (\dfrac{ - 6}{5} \times 5) + b[/tex]
[tex] \hookrightarrow \: - 7 = - 6 + b[/tex]
[tex] \hookrightarrow \: b = - 1[/tex]
now, let's put the value of m (slope) and b (y-intercept) in the equation.
[tex] \hookrightarrow \: y = mx + b[/tex]
[tex] \boxed{ \boxed{\: y = \dfrac{ - 6}{5}x - 1 }}[/tex]
That's All, I hope it helped ya
