Question

A line has this equation: x + y = 6

Write an equation for the perpendicular line that goes through (5, 1).

Answer 1

the equation of the line will be:
`y=x-4`

Explanation:

Equation of line: x + y = 6

We need to write an equation for the perpendicular line that goes through

(5, 1).

The equation will be in slope-intercept form
`y=mx+b` where m is slope and b is y-intercept

Finding Slope:

Equation of line given is: x+y=6

Writing it in slope-intercept form:
`y=-x+6`

The slope of this line is m = -1 (By comparing it with
`y=mx+b` we get m = -1)

Since the required line is perpendicular, their slopes will be opposite inverse of each other i.e.
`m_1=-(1)/(m_1)`

So, slope of required line will be: m=1

Now, using the point (5,1) and slope m=1 we can find y-intercept

`y=mx+b\\1=1(5)+b\\1=5+b\\b=1-5\\b=-4`

So, we get y-intercept b = -4

Now, the equation of required line, having slope m=1 and y-intercept b = -4

`y=mx+b\\y=1x-4`

So, the equation of the line will be:
`y=x-4`