Question

Please help me with this!

Answer 1

y - 5 =
`(1)/(4)` (x - 8 )

Explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

m is the slope and (a, b ) a point on the line

given g(- 4) = 2 , means when x = - 4 , then y = 2

g(8) = 5 , means when x = 8 , then y = 5

Thus we have 2 points on the line , that is (- 4, 2 ) and (8, 5 )

calculate the slope m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

let (x₁, y₁ ) = (- 4, 2 ) and (x₂, y₂ ) = (8, 5 )

substitute these values into the formula for m

m =
`(5-2)/(8-(-4))` =
`(3)/(8+4)` =
`(3)/(12)` =
`(1)/(4)`

Use any of the 2 points for (a, b )

using (a, b ) = (8, 5 ) , then

y - 5 =
`(1)/(4)` (x - 8 )