Answered

Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Find reliable answers to your questions from a wide community of knowledgeable experts on our user-friendly Q&A platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

2) write the equation of a line that passes through the point ( 4, 5) and is perpendicular to a line that passes through the points ( 6 8) and (10 0)

Sagot :

We have the following:

First we calculate the slope of the line where we are given two points (6,8) and (10,0)

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

repplacing:

[tex]m=\frac{0-8}{10-6}=\frac{-8}{4}=-2[/tex]

now, when two lines are perpendicular:

[tex]\begin{gathered} m_1=-\frac{1}{m_2} \\ -2=-\frac{1}{m_2} \\ 2=\frac{1}{m_2} \\ m_2=\frac{1}{2} \end{gathered}[/tex]

now,

[tex]y=mx+b[/tex]

with the point (4,5), replacing:

[tex]\begin{gathered} 5=\frac{1}{2}\cdot4+b \\ 5=2+b \\ b=5-2 \\ b=3 \end{gathered}[/tex]

Therefore, the equation is:

[tex]\begin{gathered} y=\frac{1}{2}x+3 \\ y=\frac{x}{2}+3 \end{gathered}[/tex]

check:

[tex]\begin{gathered} y=\frac{4}{2}+3 \\ y=2+3 \\ y=5 \end{gathered}[/tex]

Therefore, the answer is y = x/2 + 3

We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.