Respuesta :
Answer:
y = [tex]\frac{2}{3}[/tex] x - 1
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 the slope m, using the slope formula
• m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
let (x₁, y₁ ) = (12, 7 ) and (x₂, y₂ ) = (21, 13 )
substitute these values into the formula for m
m = [tex]\frac{13-7}{21-12}[/tex] = [tex]\frac{6}{9}[/tex] = [tex]\frac{2}{3}[/tex] , then
y = [tex]\frac{2}{3}[/tex] x + c ← is the partial equation
To find c, substitute either of the 2 points into the partial equation.
using (21, 13 ) for x and y in the partial equation
13 = [tex]\frac{2}{3}[/tex] (21) + c = 14 + c ( subtract 14 from both sides )
- 1 = c
y = [tex]\frac{2}{3}[/tex] x - 1 ← equation of line
