A line has this equation: x + y = 6 Write an equation for the perpendicular line that goes through (5, 1).

the equation of the line will be:

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 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:

The slope of this line is m = -1 (By comparing it with we get m = -1)

Since the required line is perpendicular, their slopes will be opposite inverse of each other i.e.

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

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

So, we get y-intercept b = -4

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

So, the equation of the line will be:

I think the answer is C hope this helps.