Question

How do you write the equation of the line which has y-intercept (0, 5) and is perpendicular to the line with equation y = –3x + 1?

Answer 1

`y=1/3x+5`

Explanation:

The equation of a line in `color(blue)"slope-intercept form"` is

`color(red)(|bar(ul(color(white)(a/a)color(black)(y=mx+b)color(white)(a/a)|)))`
where m represents the gradient and b, the y-intercept.

The advantage of having the line in this form is that m and b can be extracted 'easily'

The equation : y = - 3x + 1 is in this form

hence m = - 3

If 2 lines are perpendicular then the product of their gradients .
`m_1" and " m_2", say,"` is -1

`color(red)(|bar(ul(color(white)(a/a)color(black)(m_1.m_2=-1)color(white)(a/a)|)))`

hence gradient of perpendicular line is `1/3" since "(3xx-1/3=-1)`

We have y-intercept = b = 5 and m `=1/3`

`rArry=1/3x+5" is the equation"`
graph{(y+3x-1)(y-1/3x-5)=0 [-20, 20, -10, 10]}