To write the equation of a line you need to identify the slope (m) and the y-intercept (b).
[tex]y=mx+b[/tex]Slope:
Two perpendicular lines have opposite slopes, as you have the nexrt equation for a perpendicular line to k:
[tex]4y-x=2[/tex]Write it as y=mx+b to identify the slope (solve y):
[tex]\begin{gathered} 4y=x+2 \\ y=\frac{1}{4}x+\frac{2}{4} \\ \\ y=\frac{1}{4}x+\frac{1}{2} \end{gathered}[/tex]The slope of the line above is 1/4. Then, the slope of line k is the opposite of 1/4.
Slope of K: m= -1/4Y-intercept:
To find the y intercept use the given point (1,2) and the slope in the equation:
[tex]y=mx+b[/tex]y= 2
x= 1
m= -1/4
Find b:
[tex]\begin{gathered} 2=-\frac{1}{4}(1)+b \\ \\ 2=-\frac{1}{4}+b \\ \\ 2+\frac{1}{4}=b \\ \\ \frac{9}{4}=b \end{gathered}[/tex]Y-intercept of K: b= 9/4Equation of line k:[tex]y=-\frac{1}{4}x+\frac{9}{4}[/tex]