y = - [tex]\frac{1}{2}[/tex] x + 3
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
to calculate m use the gradient formula
m = ( y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 6, 6 ) and (x₂, y₂ ) = (- 2, 4 )
m = [tex]\frac{4-6}{-2+6}[/tex] = [tex]\frac{-2}{4}[/tex] = - [tex]\frac{1}{2}[/tex]
y = - [tex]\frac{1}{2}[/tex] x + c is the partial equation
to find c substitute either of the 2 points into the partial equation
using (- 2, 4 ), then
4 = 1 + c ⇒ c = 4 - 1 = 3
y = - [tex]\frac{1}{2}[/tex] x + 3 ← in slope-intercept form
