Question

If line k is perpendicular to 4y-x=2 at point (1,2),what is the equation of link k

Answer 1

To write the equation of a line you need to identify the slope (m) and the y-intercept (b).

`y=mx+b`

Slope:

Two perpendicular lines have opposite slopes, as you have the nexrt equation for a perpendicular line to k:

`4y-x=2`

Write it as y=mx+b to identify the slope (solve y):

`\begin{gathered} 4y=x+2 \\ y=(1)/(4)x+(2)/(4) \\ \\ y=(1)/(4)x+(1)/(2) \end{gathered}`

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= -1/4

Y-intercept:

To find the y intercept use the given point (1,2) and the slope in the equation:

`y=mx+b`

y= 2

x= 1

m= -1/4

Find b:

`\begin{gathered} 2=-(1)/(4)(1)+b \\ \\ 2=-(1)/(4)+b \\ \\ 2+(1)/(4)=b \\ \\ (9)/(4)=b \end{gathered}`Y-intercept of K: b= 9/4Equation of line k:
`y=-(1)/(4)x+(9)/(4)`