Answer:
b = -21
Step-by-step explanation:
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
b - y-intercept → (0, b)
We have the points J(-4, -5) and K(-6, 3).
The points J, K and y-intercept A(0, b) are collinear. Therefore the slope of JA and KA are the same.
We have the equation:
[tex]\dfrac{b-(-5)}{0-(-4)}=\dfrac{b-3}{0-(-6)}\\\\\dfrac{b+5}{4}=\dfrac{b-3}{6}\qquad\text{cross multiply}\\\\6(b+5)=4(b-3)\qquad\text{use the distributive property}\\\\6b+30=4b-12\qquad\text{subtract 30 from both sides}\\\\6b=4b-42\qquad\text{subtract 4b from both sides}\\\\2b=-42\qquad\text{divide both sides by 2}\\\\b=-21[/tex]
