Question

A line has this equation: x + y = 6

Answer 1

Answer:

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

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 $y=mx+b$ 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. $m_1=-\frac{1}{m_1}$

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: $y=x-4$