Answer:
y = [tex]\frac{5}{6}[/tex] x + [tex]\frac{8}{3}[/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 ) = (- 2, 1) and (x₂, y₂ ) = (4, 6)
m = [tex]\frac{6-1}{4+2}[/tex] = [tex]\frac{5}{6}[/tex] , thus
y = [tex]\frac{5}{6}[/tex] x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (4, 6 ), then
6 = [tex]\frac{20}{6}[/tex] + c ⇒ c = 6 - [tex]\frac{20}{6}[/tex] = [tex]\frac{16}{6}[/tex] = [tex]\frac{8}{3}[/tex]
y = [tex]\frac{5}{6}[/tex] x + [tex]\frac{8}{3}[/tex] ← equation of line
