we are asked to determine the slope of the line that passes through the points (0, 3) and (2, -1). To do that we need to use the formula for the slope of a line:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where:
[tex]\begin{gathered} (x_1,y_1)=(0,3) \\ (x_2,y_2)=(2,-1) \end{gathered}[/tex]Replacing in the formula:
[tex]m=\frac{-1-3}{2-0}[/tex]Solving the operations:
[tex]m=-\frac{4}{2}=-2[/tex]therefore, the slope is -2.
To determine the y-intercept we can use the point (0,3), since this means that when x = 0, y = 3. Since the y-intercept is the value of "y" when x = 0, this means that the y-intercept is 3.
To determine the equation of the line we need to use the general form of a line equation:
[tex]y=mx+b[/tex]Where "m" is the slope and "b" the y-intercept. Replacing the value of the slope and "b"
[tex]y=-2x+3[/tex]
