Answer:
[tex]2y-3x=-8[/tex]
Explanation:
Given the graph in the attached image;
The intercept of the line on the y-axis is at;
[tex]\begin{gathered} y=-4 \\ At\text{ point;} \\ (0,-4) \\ \text{ intercept b is;} \\ b=-4 \end{gathered}[/tex]
At the x=2, the value of y is;
[tex]\begin{gathered} y=-1 \\ at\text{ point;} \\ (2,-1) \\ \end{gathered}[/tex]
The slope of the line can be calculated using the two points on the graph;
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-1-(-4)}{2-0}=\frac{-1+4}{2} \\ m=\frac{3}{2} \end{gathered}[/tex]
The slope intercept equation of a straight line is of the form;
[tex]y=mx+b[/tex]
substituting the slope m and intercept b we have;
[tex]y=\frac{3}{2}x-4[/tex]
As this is not among the given options, let us solve further;
multiply through by 2 and move the x term to the left side;
[tex]\begin{gathered} y(2)=\frac{3}{2}x(2)-4(2) \\ 2y=3x-8 \\ 2y-3x=-8 \end{gathered}[/tex]
Therefore, from the given options the correct equation for the line is C;
[tex]2y-3x=-8[/tex]
