Hello!
To write this equation, let's first find the slope using the formula [tex] \frac{y_{2} - y_{1} }{x_{2} - x_{1}} [/tex].
Plug in the values
[tex] \frac{6 - 9}{4 - 3} [/tex]
Now solve to find our slope.
[tex] \frac{6 - 9}{4 - 3} = \frac{-3}{1}[/tex]
Your slope is -3.
Plug that into slope-intercept equation.
[tex]y = -3x + b[/tex]
Now we find our y-intercept by plugging in a y-coordinate for the y value in the equation. I'll use 6
[tex]4 = -3x + 6 6 = -3(4) + b
6 = -12 + b
6/6 = -12/6 + b
-2 = b[/tex]
Your y-intercept is -2.
Your equation is y = -3x - 2
