To find the equation, use the slope intercept form:
y = mx + b
where m is the slope and b is the y-intercept
Take the points on the graph:
(x1, y1) ==> (3, -4)
(x2, y2) ==> (0, -2)
Find the slope using the formula below:
[tex]m\text{ = }\frac{y2-y1}{x2\text{ - x1}}[/tex][tex]m\text{ = }\frac{-2-(-4)}{0-3}=\frac{-2+4}{0-3}=\frac{2}{-3}\text{ = -}\frac{2}{3}[/tex]
The y-intercept is the point where the line crosses the y-axis.
The y-intercept here is -2.
Therefore, we have the equation:
[tex]y\text{ = -}\frac{2}{3}x\text{ - 2}[/tex]
Now, equate the equation above to zero:
[tex]-y-\frac{2}{3}x-2\text{ = 0}[/tex]
Multiply through by -3, to eliminate the fraction:
[tex]\begin{gathered} -y(-3)\text{ -}\frac{2}{3}x(-3)\text{ -2(-3) = 0} \\ \\ 3y\text{ + 2x + 6 = 0} \end{gathered}[/tex]
Therefore, the equation that represents the graph is:
3y + 2x + 6 = 0
ANSWER:
A) 3y + 2x + 6 = 0
