The value of [tex]m= \frac{- 1}{6}[/tex] and [tex]b = 5[/tex]
Solution:
Given, Line passes through points [tex]A(-6,6) = (x_1, y_1); \ B(12,3) = (x_2 , y_2)[/tex]
Slope of line passing through two points is [tex]m = \frac{(y_2-y_1)}{(x_2-x_1)}[/tex]
[tex]\rightarrow \frac{(3-6)}{(12- (-6))}[/tex]
[tex]\rightarrow \frac{-3}{18} = \frac{-1}{6}[/tex]
Equation of a straight line passing through point-slope form is [tex]y - y1 = m (x - x1) --- (1)[/tex]
Since we have two points we can use any point. Let us take [tex]A (-6,6)[/tex] and m [tex]\frac{-1}{6}[/tex] and substitute in (1)
[tex]\Rightarrow y - 6 = \frac{-1}{6 (x - (-6))}[/tex]
[tex]\Rightarrow y - 6 = \frac{-1}{6x -1}[/tex]
[tex]\Rightarrow y = \frac{-1}{6x + 5}[/tex] [By equating as [tex]y = mx + b[/tex]]
[tex]m = \frac{-1}{6} ; b = 5[/tex]
Substituting the other coordinates also gives the same result.
