Answer:
y=3x-21
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,
, of line AB, use the slope formula:




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:


Substituting values for a known point (point A) on line AB...



Finding a common denominator...



So, the equation for line AB is

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.




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:


Substituting values for a known point (point B) on line BC...




So, the equation for line BC is
