The equation of the line in slope-intercept form is,
[tex]y=mx_{}+b[/tex]
where,
m = slope
The equation of the line given is,
[tex]x+y=1[/tex]
Let us now rearrange the equation in the slope-intercept form in order to obtain the slope.
Therefore,
[tex]\begin{gathered} x+y=1 \\ y=-x+1 \\ \therefore\text{ The slope(m) is -1.} \end{gathered}[/tex]
We were told the point is parallel to the equation of the line.
The rule for parallelism is,
[tex]\begin{gathered} m_1=m_2 \\ \therefore-1=-1 \end{gathered}[/tex]
The formula to calculate for the equation of a line given one point is,
[tex]y-y_1=m(x-x_1)[/tex]
Given
[tex]\begin{gathered} (x_1,y_1)=(4,2) \\ m=-1 \end{gathered}[/tex]
Substitute and simplify
[tex]\begin{gathered} y-2=-1(x-4) \\ y-2=-1x+4 \\ y=-x+4+2 \\ \therefore y=-x+6 \end{gathered}[/tex]
Hence, the equation of the line in slope-intercept form is
[tex]y=-x+6[/tex]
