Question

How do you find the point-slope form of the equation of the line passing through the points (-3, 2) and (2, 1)?

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;

`(1-2)/(2-(-3)) = -1/5`

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

We should use one point to find the real equation. If we use (2,1) point;
`y= ax+b => 1=2a+b`;
a is the slope of the equation, we found that as `-1/5`;
`1=(2*-1/5) + b => 1=-2/5 +b => b=1+2/5=7/5`;
So the equation of the line will be;
`y=ax+b => ul (y= -x/5+7/5)`
We can check if our equation is right or not with other given point;
#(-3,2) => y=-x/5+7/5 => 2=-1/5(-3)+7/5 => 2=3/5 + 7/5 => 2= 10/5 => 2=2 #
So the equation is correct :)