Answer:
the equation of the line will be: [tex]y=x-4[/tex]
Step-by-step 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 [tex]y=mx+b[/tex] 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: [tex]y=-x+6[/tex]
The slope of this line is m = -1 (By comparing it with [tex]y=mx+b[/tex] we get m = -1)
Since the required line is perpendicular, their slopes will be opposite inverse of each other i.e. [tex]m_1=-\frac{1}{m_1}[/tex]
So, slope of required line will be: m=1
Now, using the point (5,1) and slope m=1 we can find y-intercept
[tex]y=mx+b\\1=1(5)+b\\1=5+b\\b=1-5\\b=-4[/tex]
So, we get y-intercept b = -4
Now, the equation of required line, having slope m=1 and y-intercept b = -4
[tex]y=mx+b\\y=1x-4[/tex]
So, the equation of the line will be: [tex]y=x-4[/tex]
