Question

What is the equation of the line in standard form?

Answer 1

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 = $\frac{-1-2}{2+3}$ = - $\frac{3}{5}$

y = - $\frac{3}{5}$ x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (2, - 1), then

- 1 = - $\frac{6}{5}$ + c ⇒ c = - 1 + $\frac{6}{5}$ = $\frac{1}{5}$

y = - $\frac{3}{5}$ x + $\frac{1}{5}$ ← in slope-intercept form

multiply all terms by 5

5y = - 3x + 1 ( add 3x to both sides )

3x + 5y = 1 ← in standard form

Answer 2

(-3, 2) & (2, -1):

• Y2 is -1
• Y1 is 2
• X2 is 2
• X1 is -3

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!!! :)