Question

How do you find the point-slope form of the equation of the line passing through the points (4,2), (-4, -2)?

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;

`(-2-2)/(-4-4) = (-4)/-8 = 1/2`

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

We should use one point to find the real equation. If we use (4,2) point;
`y= ax+b => 2=4a+b`;
a is the slope of the equation, we found that as `1/2`;
`2=(4*1/2) + b => 2=2 +b => b=0`;
So the equation of the line will be;
`y=ax+b => ul (y= x/2)`
We can check if our equation is right or not with other given point;
`(-4,-2) => y=x/2 => -2=-4/2 => -2=-2`
So the equation is correct :)