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