Question

How do you find the point-slope form of the equation of the line passing through the points x(3, 2) and y(5,10)?

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;

`(10-2)/(5-3) = 8/2 = 4`

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

We should use one point to find the real equation. If we use (3,2) point;
`y= ax+b => 2=3a+b`;
a is the slope of the equation, we found that as `4`;
`2=(3*4) + b => 2=12 +b => b=-10`;
So the equation of the line will be;
`y=ax+b => ul (y= 4x-10)`
We can check if our equation is right or not with other given point;
#(5,10) => y=4x-10 => 10=(4*5)-10 => 10=20-10 => 10=10#
So the equation is correct :)