Answer:
y = - [tex]\frac{5}{2}[/tex] x + [tex]\frac{21}{2}[/tex]
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 ) = (1, 8) and (x₂, y₂ ) = (3, 3)
m = [tex]\frac{3-8}{3-1}[/tex] = - [tex]\frac{5}{2}[/tex] , thus
y = - [tex]\frac{5}{2}[/tex] x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (1, 8), then
8 = - [tex]\frac{5}{2}[/tex] + c ⇒ c = 8 + [tex]\frac{5}{2}[/tex] = [tex]\frac{21}{2}[/tex]
y = - [tex]\frac{5}{2}[/tex] x + [tex]\frac{21}{2}[/tex] ← equation of line
