Answer:
[tex]y = -\frac{2}{5}\cdot x - 11[/tex]
Step-by-step explanation:
First, the slope is determined by using the following expression:
[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m = \frac{-7-(-9)}{-10 - (-5)}[/tex]
[tex]m = -\frac{2}{5}[/tex]
The y-intercept is found by using the line equation, the slope and one point:
[tex]y = m \cdot x +b[/tex]
[tex]b = y - m\cdot x[/tex]
[tex]b = -7 - \left(-\frac{2}{5}\right)\cdot (-10)[/tex]
[tex]b = -11[/tex]
The equation of the line is:
[tex]y = -\frac{2}{5}\cdot x - 11[/tex]
