Question

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

Answer 1

Answer: first option

Step-by-step 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:

 $m=\frac{y_2-y_1}{x_2-x_1}$

Choose two points of the line and substitute values.

Points:(-3,0) and  (3,-4)

Then:

 $m=\frac{-4-0}{3-(-3)}=-\frac{2}{3}$

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

 $y=-\frac{2}{3}x+2$

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

$y=\frac{-2x+6}{3}$

Multiply both sides of the equation by 3:

$3(y)=(3)(\frac{-2x+6}{3})$

$3y=-2x+6$

And finally add 2x to both sides:

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

$2x+3y=6$