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