Question

Line jk passes through points j(-4,-5) and k(-6,3). What is the value of b

Answer 1

b = -21

Explanation:

The formula of a slope:

`m=(y_2-y_1)/(x_2-x_1)`

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:

`(b-(-5))/(0-(-4))=(b-3)/(0-(-6))\\\\(b+5)/(4)=(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`