# Difference between revisions of "008A Sample Final A, Question 15"

Question: a) Find the equation of the line passing through (3, -2) and (5, 6).
b) Find the slope of any line perpendicular to your answer from a)

Foundations:
1) We have two points on a line. How do we find the slope?
2) How do you write the equation of a line, given a point on the line and the slope?
3) For part b) how are the slope of a line and the slope of all perpendicular lines related?
1) The formula for the slope of a line through two points ${\displaystyle (x_{1},y_{1})}$  and  ${\displaystyle (x_{2},y_{2})}$   is  ${\displaystyle {\frac {y_{2}-y_{1}}{x_{2}-x_{1}}}}$.
2) The point-slope form of a line is ${\displaystyle y-y_{1}=m(x-x_{1})}$ where the slope of the line is m, and ${\displaystyle (x_{1},y_{1})}$ is a point on the line.
3) If m is the slope of a line. The slope of all perpendicular lines is ${\displaystyle {\frac {-1}{m}}}$
Since the slope of a line passing through two points is ${\displaystyle {\frac {y_{2}-y_{1}}{x_{2}-x_{1}}}}$, the slope of the line is ${\displaystyle {\frac {6-(-2)}{5-3}}={\frac {8}{2}}=4}$
Now that we have the slope of the line and a point on the line the equation for the line is ${\displaystyle y-6=4(x-5)}$. Another answer is ${\displaystyle y+2=4(x-3)}$. These answers are the same. They just look different.
Since the slope of the line in part a) is 4, the slope of any line perpendicular to the answer in a) is ${\displaystyle {\frac {-1}{4}}}$