Respuesta :
Lets find the equation of the line. The equation of the line that passes through a point is:
[tex]y-y_0=m(x-x_0)[/tex]where x_0 and y_0 are the coordinates of the point and m is the slope.
Then, in this case m = 2 and the point (-1, 3)
We can write:
[tex]y-3=2(x-(-1))[/tex]And solve for y:
[tex]\begin{gathered} y=2x+2+3 \\ \end{gathered}[/tex]The equation of the line is:
[tex]y=2x+5[/tex]Now to see which of the options is a point in the line, we evaluate each x coordinate to see if give us the correct y coordinate.
The option a is (1, 4)
[tex]\begin{gathered} y=2\cdot1+5 \\ y=7 \end{gathered}[/tex]Option a cannot be.
Option b is (-3, 2)
[tex]\begin{gathered} y=2\cdot(-3)+5 \\ y=-6+5 \\ y=-1 \end{gathered}[/tex]Option b cannot be either
Option c is (1, 5) but we already know that the y coordinate when x = 1 is 7. C cannot be.
Finally, option D is (0, 5)
[tex]\begin{gathered} y=2\cdot0+5 \\ y=5 \end{gathered}[/tex]Wich is correct.
Thus, the correct answer is option D.
