What is the equation of the graphed line written in standard form?

a)2x + 3y = –6
b)2x + 3y = 6
c)y equals negative startfraction 2 over 3 endfraction x minus 2.
d)y equals startfraction 2 over 3 endfraction x minus 2.

Option A) 2x + 3y = –6

Step-by-step explanation:

step 1

Find the slope of the line

The formula to calculate the slope between two points is equal to

we have the points

(0,-2) ---> y-intercept

(-3,0) ---> x-intercept

substitute in the formula

step 2

Find the equation of the line in slope intercept form

where

m is the slope

b is the y-intercept

we have

substitute

step 3

Convert to standard form

The equation of the line in standard form is equal to

where

A is a positive integer

B and C are integers

we have

Multiply by 3 both sides to remove the fraction

Adds 2x both sides

----> equation in standard form