Answer:
The value of b is 5.
Step-by-step explanation:
Given: Line AB passes through points A(-6,6) and B(12,3).
Slope- intercept form:-The equation of a line with slope m and making an intercept b on y -axis is y = mx + b.
Since the line passes through two points therefore, we can use the Two Point Form formula:
[tex]y-y_{1}=m(x-x_{1})[/tex] ; where m is the slope.
or Slope [tex]m =\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
First find the value of m using the points A(-6,6) and B(12,3) ;
[tex]m = \frac{3-6}{12-(-6)} = \frac{-3}{18} =\frac{-1}{6}[/tex]
Now, the equation of line AB :-
[tex]y-6=\frac{-1}{6}(x+6)[/tex] or
[tex]y-6 =\frac{-1}{6} x-\frac{6}{6}[/tex] or
[tex]y-6=\frac{-1}{6} x-1[/tex] or
[tex]y=\frac{-1}{6}x-1+6[/tex]
Simplify:
[tex]y = \frac{-1}{6}x+5[/tex]
Comparing above equation with the general equation of line i.e, y = mx+b , we get;
[tex]m= \frac{-1}{6}[/tex] and b= 5
Therefore, the value y-intercept (b) = 5