Question

How do you write the equation of a line in point slope form and slope intercept form given points (6, -4) (-3, 5) ?

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;

`(5-(-4))/(-3-6) = 9/-9 = -1`

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

We should use one point to find the real equation. If we use (-3,5) point;
`y= ax+b => 5=-3a+b`;
a is the slope of the equation, we found that as `-1`;
`5=(-3*-1) + b => 5=3 +b => b=2`;
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;
`(6,-4) => y=-x+2 => -4=-(-1*6)+2 => -4=-6+2 =>-4=-4`
So the equation is correct :)