Answer:
y = - [tex]\frac{7}{3}[/tex] x + [tex]\frac{5}{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 = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (2, - 3) and (x₂, y₂ ) = (- 1, 4)
m = [tex]\frac{4+3}{-1-2}[/tex] = [tex]\frac{7}{-3}[/tex] = - [tex]\frac{7}{3}[/tex], thus
y = - [tex]\frac{7}{3}[/tex] x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (- 1, 4), then
4 = [tex]\frac{7}{3}[/tex] + c ⇒ c = 4 - [tex]\frac{7}{3}[/tex] = [tex]\frac{5}{3}[/tex]
y = - [tex]\frac{7}{3}[/tex] x + [tex]\frac{5}{3}[/tex] ← equation of line
