Given that the slope of a line is 2/3, that passes through the point (4, -1), i.e
[tex]\begin{gathered} m=\frac{2}{3} \\ (x_1,y_1)\Rightarrow(4,-1) \end{gathered}[/tex]
The formula to find the equation of straight line is
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{Where m is the slope of the line} \end{gathered}[/tex]
Substitute the values into the formula of the equation of a straight line
[tex]y-(-1)=\frac{2}{3}(x-4)[/tex]
Solve for y i.e make y the subject
[tex]\begin{gathered} y-(-1)=\frac{2}{3}(x-4) \\ y+1=\frac{2}{3}(x-4) \\ \text{Open the bracket} \\ y+1=\frac{2}{3}x-\frac{2}{3}(4) \\ y+1=\frac{2}{3}x-\frac{8}{3} \\ y=\frac{2}{3}x-\frac{8}{3}-1 \\ y=\frac{2}{3}x-(\frac{8}{3}+1) \\ y=\frac{2}{3}x-(\frac{8+3}{3}) \\ y=\frac{2}{3}x-\frac{11}{3} \end{gathered}[/tex]
Thus, the answer is
[tex]y=\frac{2}{3}x-\frac{11}{3}[/tex]
Thus, the answer is the last option.
