Question

4. Ifline m has the equation y = 3x - 1, and line k is perpendicular to m and goes through the point (-4,3), find the equation of line k.

Answer 1

The equation of the line k is

`y=-(1)/(3)x+(5)/(3)`

Step-by-step explanation:

Given that k is perpendicular to line m, defined as:

y = 3x - 1

the slope of k is the negative reciprocal of the slope of line m.

The slope of m is 3

The negative reciprocal of m is -1/3 (this is the slope of k)

Therefore, k is in the form

`y=-(1)/(3)x+b`

Since this line passes through the point (x, y) = (-4, 3), we can use this to obtain the value for the y-intercept, b

`\begin{gathered} 3=-(1)/(3)(-4)+b \\ \\ 3=(4)/(3)+b \end{gathered}`

Solving for b by subtracting 4/3 from both sides

`\begin{gathered} b=3-(4)/(3) \\ \\ =(5)/(3) \end{gathered}`

The equation is therefore,

`y=-(1)/(3)x+(5)/(3)`