Answer:
3x + 5y = 1
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 )
Obtain the equation in slope- intercept form
y = mx + c ( m is the slope and c the y-intercept )
to calculate m use the gradient formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (- 3, 2) and (x₂, y₂ ) = (2, - 1) ← 2 points on the line
m = [tex]\frac{-1-2}{2+3}[/tex] = - [tex]\frac{3}{5}[/tex]
y = - [tex]\frac{3}{5}[/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{6}{5}[/tex] + c ⇒ c = - 1 + [tex]\frac{6}{5}[/tex] = [tex]\frac{1}{5}[/tex]
y = - [tex]\frac{3}{5}[/tex] x + [tex]\frac{1}{5}[/tex] ← in slope-intercept form
multiply all terms by 5
5y = - 3x + 1 ( add 3x to both sides )
3x + 5y = 1 ← in standard form
(-3, 2) & (2, -1):
Y2 - Y1
X2 - X1
-1 - 2
2 - - 3
-3
5
y - Y1 = m(x - X1)
y - 2 = -3/5(x - -3) --- POINT SLOPE FORM
y - 2 = -3/5(x + 3)
y - 2 = -3/5x - 1.8
+ 2 + 2
y = -3/5x + 0.2 --- SLOPE INTERCEPT FORM
+3/5x + 3/5x
3/5x + y = 0.2 --- STANDARD FORM
Hope this helps you!!! :)
