Answer:
y = - x + 5
Step-by-step explanation:
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 ) = (4, 1) and (x₂, y₂ ) = (- 2, 7)
m = [tex]\frac{7-1}{-2=4}[/tex] = [tex]\frac{6}{-6}[/tex] = - 1, hence
y = - x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
using (4, 1), then
1 = - 4 + c ⇒ c = 1 + 4 = 5
y = - x + 5 ← equation of line
