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

b = - 21

Explanation:

calculate m using the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

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

m =
`(3+5)/(-6+4)` =
`(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

Explanation:

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

`(y-b)=(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))=(3-(-5))/(-6-(-4))(x-(-4))\\\\\Rightarrow\ (y+5)=(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`