Answer:
[tex]\boxed{y = -\dfrac{10}{3}x - 23}[/tex]
Step-by-step explanation:
Equation of a straight line: y = kx + b
Points: (-9,7) and (-6,-3)
Сompose the system of equations:
[tex]\displaystyle \left \{ {{7=-9k + b} \atop {-3=-6k + b}} \right[/tex] [tex]\displaystyle \left \{ {{b= 7 + 9k} \atop {b=6k - 3}} \right \Longrightarrow 7 + 9k = 6k - 3[/tex]
[tex]7 + 9k = 6k - 3[/tex]
[tex]3k = -10|:3[/tex]
[tex]k = -\dfrac{10}{3}[/tex]
[tex]b = 6k - 3= 6 \cdot \dfrac{-10}{3} - 3 = 2 \cdot (-10) - 3 = -20 - 3 = -23[/tex]
[tex]y = -\dfrac{10}{3}x - 23[/tex]
