Answer:
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
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have the points
(0,-2) ---> y-intercept
(-3,0) ---> x-intercept
substitute in the formula
[tex]m=\frac{0+2}{-3-0}[/tex]
[tex]m=\frac{2}{-3}[/tex]
[tex]m=-\frac{2}{3}[/tex]
step 2
Find the equation of the line in slope intercept form
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-intercept
we have
[tex]m=-\frac{2}{3}[/tex]
[tex]b=-2[/tex]
substitute
[tex]y=-\frac{2}{3}x-2[/tex]
step 3
Convert to standard form
The equation of the line in standard form is equal to
[tex]Ax+By=C[/tex]
where
A is a positive integer
B and C are integers
we have
[tex]y=-\frac{2}{3}x-2[/tex]
Multiply by 3 both sides to remove the fraction
[tex]3y=-2x-6[/tex]
Adds 2x both sides
[tex]2x+3y=-6[/tex] ----> equation in standard form
