Question

How do you write an equation in slope intercept form given that the line passes through (-2,-1) and (3,-4)?

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;

`(-4-(-1))/(3-(-2)) = -3/5`

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

We should use one point to find the real equation. If we use (3,-4) point;
`y= ax+b => -4=3a+b`;
a is the slope of the equation, we found that as `-3/5`;
`-4=(3*-3/5) + b => -4=-9/5 +b => b=-4+9/5 =(-20+9)/5 => b= -11/5`;
So the equation of the line will be;
`y=ax+b => ul (y= -3/5x-11/5)`
We can check if our equation is right or not with other given point;
`(-2,-1) => y=-3/5x-11/5 => -1=-3/5*(-2)-11/5 => -1=6/5-11/5 => -1=-5/5 =>-1=-1`
So the equation is correct :)