Respuesta :
We are asked to find the equation in slope-intercept form that passes through the following points.
[tex](0,3)\text{ and }(2,-1)[/tex]Recall that the equation of the line in slope-intercept form is given by
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
The slope of the line is given by
[tex]m=\frac{y_2−y_1}{ x_2−x_1}[/tex][tex]\text{where}(x_1,y_1)=(0,3)\text{and}(x_2,y_2)=(2,-1)[/tex]Let us substitute the given values into the above slope formula
[tex]m=\frac{-1-3}{2-0}=-\frac{4}{2}=-2[/tex]So the equation of line becomes
[tex]y=-2x+b[/tex]Now let us find the y-intercept (b)
Choose any one point from the given two points
Let choose (0, 3) and substitute it into the above equation.
[tex]\begin{gathered} y=-2x+b \\ 3=-2(0)+b \\ 3=0+b \\ 3=b \\ b=3 \end{gathered}[/tex]Please note that even if you had chosen any other point then still you would have gotten the same y-intercept.
Therefore, the equation of the line in slope-intercept form is
[tex]y=-2x+3[/tex]The correct option is A.
