The general form of equation of line passing through two points is :
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]we have :
[tex](x_1,y_1)=(1,-2)(x_2,y_2)\text{ =(4,7)}[/tex]Substitute these value in the genral form of line:
[tex]\begin{gathered} y-(-2)=\frac{7-(-2)}{4-1}(x-1) \\ y+2=\frac{7+2}{3}(x-1) \\ y+2=\frac{9}{3}(x-1) \\ y+2=3(x-1) \\ y+2=3x-3 \\ 3x-y=2+3 \\ 3x-y=5 \\ 3x-y-5=0 \\ \text{Solve the equation in terms of y} \\ y=3x-5 \end{gathered}[/tex]The required equation of line : y = 3x - 5
Answer: D) y = 3x - 5
