Answered

At Westonci.ca, we make it easy to get the answers you need from a community of informed and experienced contributors. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

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

A Line Has This Equation X Y 6 Write An Equation For The Perpendicular Line That Goes Through 5 1 class=

Sagot :

absor201

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]

We appreciate your time. Please come back anytime for the latest information and answers to your questions. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.