Answer:
y = [tex]\frac{3}{8}[/tex] x + [tex]\frac{41}{8}[/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 )
To calculate the slope use the gradient formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (- 3, 4) and (x₂, y₂ ) = (5, 7)
m = [tex]\frac{7-4}{5+3}[/tex] = [tex]\frac{3}{8}[/tex], hence
y = [tex]\frac{3}{8}[/tex] x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
using (5, 7 ), then
7 = [tex]\frac{15}{8}[/tex] + c ⇒ c = 7 - [tex]\frac{15}{8}[/tex] = [tex]\frac{41}{8}[/tex]
y = [tex]\frac{3}{8}[/tex] x + [tex]\frac{41}{8}[/tex] ← equation in slope-intercept form
