Answer:
y = [tex]\frac{1}{2}[/tex] x + 7
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 ) = (2, 8) and (x₂, y₂ ) = (10,12) ← 2 ordered pairs from the table
m = [tex]\frac{12-8}{10-2}[/tex] = [tex]\frac{4}{8}[/tex] = [tex]\frac{1}{2}[/tex]
y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
to find c substitute any ordered pair into the partial equation
using (6, 10 ), then
10 = 3 + c ⇒ c = 10 - 3 = 7
y = [tex]\frac{1}{2}[/tex] x + 7 ← linear equation
