Question

Line JK passes through points J(–4, –5) and K(–6, 3). If the equation of the line is written in slope-intercept form, y = mx + b, what is the value of b? –21 –4 11 27

Answer 1

Answer:

b = - 21

Step-by-step explanation:

calculate m using the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (- 4, - 5) and (x₂, y₂ ) = (- 6, 3)

m = $\frac{3+5}{-6+4}$ = $\frac{8}{-2}$ = - 4

y = - 4x + b ← is the partial equation

to find b substitute either of the 2 given points into the partial equation

using (- 4, - 5 ), then

- 5 = 16 + b ⇒ b = - 5 - 16 = - 21

Answer 2

Answer: -21

Step-by-step explanation:

We know that the equation of a line passing through points (a,b) and (c,d) is given by :-

$(y-b)=\dfrac{d-b}{c-a}(x-a)$

Then , the equation of a line passing through points J(-4, -5) and K(-6, 3) is given by :-

$(y-(-5))=\dfrac{3-(-5)}{-6-(-4)}(x-(-4))\\\\\Rightarrow\ (y+5)=\dfrac{8}{-2}(x+4)\\\\\Rightarrow\ y+5=-4(x+4))\\\\\Rightarrow\ y+5=-4x-16\\\\\Rightarrow\ y=-4x-21$

Comparing to the general intercept form of equation $y = mx + b$, we get

The value of $b=-21$