Answer:
y = - [tex]\frac{6}{7}[/tex] x - [tex]\frac{10}{7}[/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 ) = (- 4, 2 ) and (x₂, y₂ ) = (3, - 4) ← 2 points on the line
m = [tex]\frac{-4-2}{3+4}[/tex] = - [tex]\frac{6}{7}[/tex] , thus
y = - [tex]\frac{6}{7}[/tex] x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (- 4, 2 ), then
2 = [tex]\frac{24}{7}[/tex] + c ⇒ c = 2 - [tex]\frac{24}{7}[/tex] = - [tex]\frac{10}{7}[/tex]
y = - [tex]\frac{6}{7}[/tex] x - [tex]\frac{10}{7}[/tex] ← equation of line
