Answer:
[tex]y = -\dfrac{1}{2} x -1[/tex]
Step-by-step explanation:
To write the equation of the line passing through the coordinate points (4,-3) and (-6,-8), we need to find the slope. We can use the slope formula, which finds the change in the y-coordinates divided by the change in the x-coordinates.
[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }=\frac{-8--3}{-6-4} =\frac{-8+3}{-10}=\frac{-5}{10}=-\frac{1}{2}[/tex]
Now, we can create a point-slope formula equation and transform it into the slope-intercept form equation. We will use the given point (4, -3) for our equation, but you can use any point on the line. (x1, y1) is a point on the line and m is our slope.
y - y1 = m(x - x1)
[tex]y - (-3) = (-\dfrac{1}{2} )(x - (4))[/tex]
[tex]y +3 = -\dfrac{1}{2} x +2[/tex]
[tex]y = -\dfrac{1}{2} x +2 -3[/tex]
[tex]y = -\dfrac{1}{2} x -1[/tex]
