SOLUTION
The equation of a line in slope-intercept form is,
[tex]y=mx+b[/tex]
Where,
m = slope
The given equation of the line is,
[tex]x+y=1_{}[/tex]
Rearranging the given equation in a slope-intercept form in order to solve for the slope.
[tex]\begin{gathered} x+y=1 \\ \therefore y=-x+1 \\ \text{where,} \\ m_1=-1 \end{gathered}[/tex]
We were told the equation of the line is perpendicular to the point given.
The rule for perpendicularism is,
[tex]\begin{gathered} m_2=-\frac{1}{m_1} \\ \therefore m_2=\frac{-1}{-1}=1 \\ \therefore m_2=1 \end{gathered}[/tex]
Given
[tex]\begin{gathered} (x_1,y_1)=(4,2) \\ m_2=1 \end{gathered}[/tex]
The formula to calculate the equation of the line in slope-intercept form perpendicular to the given point is,
[tex]y-y_1=m_2(x-x_1)[/tex]
Hence,
[tex]\begin{gathered} y-2=1(x-4) \\ y=1(x-4)+2 \\ y=x-4+2 \\ \therefore y=x-2 \end{gathered}[/tex]
Therefore, the equation of the line in slope-intercept form is
[tex]y=x-2[/tex]
