Find the information you're looking for at Westonci.ca, the trusted Q&A platform with a community of knowledgeable experts. Discover reliable solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
Answer:
y=3x-21
Step-by-step explanation:
General outline
- Find equation for line AB
- Find equation for perpendicular line BC
Step 1. Find equation for line AB
Given points A(2,5) and B(8,3), line AB must contain them.
To calculate the slope, [tex]m_{\text{AB}}[/tex], of line AB, use the slope formula:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m_{\text{AB}}=\dfrac{(3)-(5)}{(8)-(2)}[/tex]
[tex]m_{\text{AB}}=\dfrac{-2}{6}[/tex]
[tex]m_{\text{AB}}=-\frac{1}{3}[/tex]
Since the slope isn't undefined, line AB must cross the y-axis somewhere. To find the y-intercept, build and equation in slope-intercept form:
[tex]y=m_{\text{AB}}x+b_{\text{AB}}[/tex]
[tex]y=\left(-\frac{1}{3} \right) x+b_{\text{AB}}[/tex]
Substituting values for a known point (point A) on line AB...
[tex](5)=\left(-\frac{1}{3} \right) (2)+b_{\text{AB}}[/tex]
[tex]5=-\frac{2}{3} +b_{\text{AB}}[/tex]
[tex](5)+\frac{2}{3} =(-\frac{2}{3} +b_{\text{AB}})+\frac{2}{3}[/tex]
Finding a common denominator...
[tex]\frac{3}{3}*5+\frac{2}{3} =b_{\text{AB}}[/tex]
[tex]\frac{15}{3}+\frac{2}{3} =b_{\text{AB}}[/tex]
[tex]\frac{17}{3}=b_{\text{AB}}[/tex]
So, the equation for line AB is [tex]y=-\frac{1}{3} x +\frac{17}{3}[/tex]
Step 2. Find equation for line BC
Since line AB and line BC form a right angle, they are perpendicular. Perpendicular lines have slopes that are opposite (opposite sign) reciprocals (fraction flipped upside-down) of each other. Stated another way, the slopes multiply to make negative 1.
[tex]m_{\text{AB}}*m_{\text{BC}}=-1[/tex]
[tex]\left( -\frac{1}{3} \right) *m_{\text{BC}}=-1[/tex]
[tex]-3*\left( -\frac{1}{3} *m_{\text{BC}} \right) =-3*(-1)[/tex]
[tex]m_{\text{BC}} =3[/tex]
Since the slope isn't undefined, line BC must also cross the y-axis somewhere. To find the y-intercept, build and equation in slope-intercept form:
[tex]y=m_{\text{BC}}x+b_{\text{BC}}[/tex]
[tex]y=(3) x+b_{\text{BC}}[/tex]
Substituting values for a known point (point B) on line BC...
[tex](3)=3 * (8)+b_{\text{BC}}[/tex]
[tex]3=24+b_{\text{BC}}[/tex]
[tex](3)-24=(24+b_{\text{BC}})-24[/tex]
[tex]-21=b_{\text{BC}}[/tex]
So, the equation for line BC is [tex]y=3 x -21[/tex]
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.
