Answer:
[tex]y + 1 = -\dfrac{2}{3}(x -4)[/tex]
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Step-by-step explanation:
The equation of a line in point slope form is
[tex]y - y1 = m(x - x1)[/tex]
where (x1, y1) is a point on the line
If we take the point (4, - -1) on the line, the equation becomes
[tex]y - -1 = m(x - 4)\\\\y + 1 = m(x - 4)[/tex]
All we have to do is find the slope m
Slope m = rise/run
rise = difference in y-values for any two points on line
run= difference in x-values for the same two points on line
Taking points B = (-2, 3) and A = (4, -1)
Rise(going from B to A) = yA - yB = -1 - 3 = -4
Run = 4 - - 2 = 6
m = Rise/Run = -4/6 = - 2/3
Hence equation of line is
[tex]y + 1 = -\dfrac{2}{3}(x -4)[/tex]
