The point is given (3, 4) and the given line is 2x+y=1.
The line to be determined is passes through the point and the perpendicular to the given line 2x+y=1.
So the slope of the line will be
[tex]m_1\times m_2=-1[/tex][tex]m_1\times-2=-1[/tex][tex]m_1=\frac{1}{2}[/tex]
The slope-intercept form of a line is
[tex]y-y_1=m(x-x_1)[/tex][tex]y-4=\frac{1}{2}(x-3)[/tex][tex]y=\frac{1}{2}x-\frac{3}{2}+4[/tex][tex]y=\frac{1}{2}x+4-\frac{3}{2}[/tex][tex]y=\frac{1}{2}x+\frac{8-3}{2}[/tex][tex]y=\frac{1}{2}x+\frac{5}{2}[/tex]
Hence the equation in slope -intercept form of a line is
[tex]y=\frac{1}{2}x+\frac{5}{2}[/tex]
