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.
You have the first line:
[tex]=2x-4[/tex]
You can identify that the y-intercept is:
[tex]b_1=-4[/tex]
You can find the x-intercept substituting the following value of "y" into the equation of the line:
[tex]y=0[/tex]
And, after the substitution, you can solve for "x":
[tex]\begin{gathered} 0=2-4 \\ 4=2x \\ \\ \frac{4}{2}=x \\ \\ x=2 \end{gathered}[/tex]
Now you know that the first line passes through these points:
[tex]\begin{gathered} (0,-4) \\ (2,0) \end{gathered}[/tex]
Then, you can graph it.
Given the second line:
[tex]y=-\frac{1}{2}x+1[/tex]
You can identify that:
[tex]b_2=1[/tex]
And you can find the x-intercept by following the same procedure applied for the first line:
[tex]\begin{gathered} 0=-\frac{1}{2}x+1 \\ \\ -1=-\frac{1}{2}x \\ \\ (-1)(2)=-x \\ \\ -2=-x \\ x=2 \end{gathered}[/tex]
Then, this line passes through these points:
[tex]\begin{gathered} (0,1) \\ (2,0) \end{gathered}[/tex]
Now you can graph it.
See the graph below:
By definition, when the lines intersect, the solution of the System of equations is the point where the two lines intersect.
The answer is: First option.
