Question

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.

Answer 1

A

Explanation:

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Answer 2

Option A) 2x + 3y = –6

Explanation:

step 1

Find the slope of the line

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

`m=(y2-y1)/(x2-x1)`

we have the points

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

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

substitute in the formula

`m=(0+2)/(-3-0)`

`m=(2)/(-3)`

`m=-(2)/(3)`

step 2

Find the equation of the line in slope intercept form

`y=mx+b`

where

m is the slope

b is the y-intercept

we have

`m=-(2)/(3)`

`b=-2`

substitute

`y=-(2)/(3)x-2`

step 3

Convert to standard form

The equation of the line in standard form is equal to

`Ax+By=C`

where

A is a positive integer

B and C are integers

we have

`y=-(2)/(3)x-2`

Multiply by 3 both sides to remove the fraction

`3y=-2x-6`

Adds 2x both sides

`2x+3y=-6` ----> equation in standard form