Question

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

Answer 1

Answer: first option

Explanation:

The equation of the line in Slope-intercept form is:

`y=mx+b`

Where "m" is the slope and "b" is the y-intercept.

The Standard form of the equation of the line is:

`Ax + By = C`

Where A is a positive integer, and B, and C are integers.

You can observe in the graph that the line intersects the y-axis at
`y=-2`, then, "b" is:

`b=-2`

Find the slope of the line with this formula:

`m=(y_2-y_1)/(x_2-x_1)`

Choose two points of the line and substitute values.

Points:(-3,0) and (3,-4)

Then:

`m=(-4-0)/(3-(-3))=-(2)/(3)`

Substituting values into
`y=mx+b`, you get the equation of the line in Slope-intercept form:

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

To write it in Standard form, make the addition indicated:

`y=(-2x+6)/(3)`

Multiply both sides of the equation by 3:

`3(y)=(3)((-2x+6)/(3))`

`3y=-2x+6`

And finally add 2x to both sides:

`2x+3y=-2x+6+2x`

`2x+3y=6`