Answer:
4x + y = 32
Step-by-step explanation:
The equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
First obtain the equation in slope- intercept form
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 ) = (7, 4) and (x₂, y₂ ) = (5, 12)
m = [tex]\frac{12-4}{5-7}[/tex] = [tex]\frac{8}{-2}[/tex] = - 4, thus
y = - 4x + c ← is the partial equation of the line
To find c substitute either of the 2 points into the partial equation.
Using (7, 4), then
4 = - 28 + c ⇒ c = 4 + 28 = 32
y = - 4x + 32 ← in slope- intercept form
Add 4x to both sides
4x + y = 32 ← in standard form
