Question

How do you find the point-slope form of the equation of the line passing through the points (8,11), (6,16)?

Answer 1

First we have to find the slope of the equation. To find the slope we have to do;
`(y2-y1)/(x2-x1)` For our question slope is;

`(16-11)/(6-8) = 5/-2 = -5/2`

The main formula of a line is;
`y=ax+b`

We should use one point to find the real equation. If we use (6,16) point;
`y= ax+b => 16=6a+b`;
a is the slope of the equation, we found that as `-5/2`;
`16=(6*-5/2) + b => 16=-15 +b => b=31`;
So the equation of the line will be;
`y=ax+b => ul (y= -5/2x+31)`
We can check if our equation is right or not with other given point;
`(8,11) => y=-5/2+31 => 11=(-5/2*8)+31 => 11=-20+31 => 11=11`
So the equation is correct :)