Answer:
y = - [tex]\frac{1}{2}[/tex] x + 3
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 )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = A(10, - 2) and (x₂, y₂ ) = B(4, 1)
m = [tex]\frac{1+2}{4-10}[/tex] = [tex]\frac{3}{-6}[/tex] = - [tex]\frac{1}{2}[/tex] , then
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 (4, 1 )
1 = - 2 + c ⇒ c = 1 + 2 = 3
y = - [tex]\frac{1}{2}[/tex] x + 3 ← equation of line
