• Given Function A:
[tex]-4x+2y=-2[/tex]You need to remember that, by definition, the value of "y" is zero when the function intersects the x-axis.
Therefore, you need to set up that:
[tex]y=0[/tex]Substitute this value into the function and then solve for "x", in order to find the x-intercept:
[tex]\begin{gathered} -4x+2(0)=-2 \\ -4x=-2 \\ \\ x=\frac{-2}{-4} \\ \\ x=\frac{1}{2} \end{gathered}[/tex]• Given that Function B passes through these points:
[tex](0,-1),(3,2)[/tex]You need to determine the equation of the line, in order to find the x-intercept using it.
The Slope-Intercept Form of the equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope of the line and "b" is the y-intercept.
By definition, the value of "x" is zero when the function intersects the y-axis. Therefore, knowing the first point given in the exercise (whose x-coordinate is zero), you can determine that, for this line:
[tex]b=-1[/tex]Substitute "b" and the coordinates of the second point into this equation:
[tex]y=mx+b[/tex]And then solve for "m":
[tex]\begin{gathered} 2=m(3)-1 \\ 2+1=3m \\ \\ \frac{3}{3}=m \\ \\ m=1 \end{gathered}[/tex]Therefore, the equation of Function B in Slope-Intercept Form is:
[tex]y=x-1[/tex]Now you can find the x-intercept by using the procedure used for Function A:
[tex]\begin{gathered} 0=x-1 \\ x=1 \end{gathered}[/tex]You know that:
[tex]\frac{1}{2}<1[/tex]Hence, the answer is: Third option.
