Question

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

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;

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

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

We should use one point to find the real equation. If we use (4,1) point;
`y= ax+b => 1=4a+b`;
a is the slope of the equation, we found that as `2`;
`1=(4*2) + b => 1=8 +b => b=-7`;
So the equation of the line will be;
`y=ax+b => ul (y= 2x-7)`
We can check if our equation is right or not with other given point;
`(2,-3) => y=2x-7 => -3=2*2-7 => -3=4-7 => -3=-3`
So the equation is correct :)