Answer:
x - 2y = - 6
Step-by-step explanation:
the equation of a line in standard form is
Ax + By = C (A is a positive integer and B, C are integers
To begin find the equation in slope- intercept form
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 ) = (- 2, 2) and (x₂, y₂ ) = (4, 5)
m = [tex]\frac{5-2}{4+2}[/tex] = [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex], hence
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, 2), then
2 = - 1 + c ⇒ c = 2 + 1 = 3
y = [tex]\frac{1}{2}[/tex] x + 3 ← in slope- intercept form
multiply through by 2
2y = x + 6 ( subtract 2y from both sides )
0 = x - 2y + 6 (subtract 6 from both sides )
x - 2y = - 6 ← in standard form
