Answer:
b = 10
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + b ( m is the slope and b the y- intercept )
calculate slope m, using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
let (x₁, y₁ ) = (12, 16) and (x₂, y₂ ) = (20, 20) ← 2 points on the line
substitute these values into the formula for m
m = [tex]\frac{20-16}{20-12}[/tex] = [tex]\frac{4}{8}[/tex] = [tex]\frac{1}{2}[/tex] , then
y = [tex]\frac{1}{2}[/tex] x + b ← is the partial equation
to find b, substitute either of the 2 points into the partial equation
using (20, 20 ) for x and y in the partial equation
20 = [tex]\frac{1}{2}[/tex] (20) + b = 10 + b ( subtract 10 from both sides )
10 = b
Then the y- intercept, b = 10
