Answer:
[tex]y = -\frac{10}{3}x -23[/tex]
Step-by-step explanation:
Given
[tex](x_1,y_1) = (-9,7)[/tex]
[tex](x_2,y_2) = (-6,-3)[/tex]
Required
Determine the line equation
We start by calculating the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where:
[tex](x_1,y_1) = (-9,7)[/tex]
[tex](x_2,y_2) = (-6,-3)[/tex]
So, we have:
[tex]m = \frac{-3- 7}{-6 - (-9)}[/tex]
[tex]m = \frac{-3- 7}{-6 +9}[/tex]
[tex]m = \frac{-10}{3}[/tex]
[tex]m = -\frac{10}{3}[/tex]
The equation is then calculated using:
[tex]y - y_1 = m(x - x_1)[/tex] ---- Point slope form of an equation
Where:
[tex]m = -\frac{10}{3}[/tex]
[tex](x_1,y_1) = (-9,7)[/tex]
[tex]y - y_1 = m(x - x_1)[/tex] becomes
[tex]y - 7 = -\frac{10}{3}(x - (-9))[/tex]
[tex]y - 7 = -\frac{10}{3}(x +9)[/tex]
Open bracket:
[tex]y - 7 = -\frac{10}{3}x -\frac{10}{3}*9[/tex]
[tex]y - 7 = -\frac{10}{3}x -10*3[/tex]
[tex]y - 7 = -\frac{10}{3}x -30[/tex]
Collect Like Terms
[tex]y = -\frac{10}{3}x -30 + 7[/tex]
[tex]y = -\frac{10}{3}x -23[/tex]
Hence:
The equation is: [tex]y = -\frac{10}{3}x -23[/tex]
