Question

In two or more complete sentences describe the process in writing the equation of a line given two points? there are no points I just need to know the process of writing the equation if there were points. need answer ASAP

Answer 1

Given the two points
`(x_(1),y_(1))` and
`(x_(2),y_(2))`, we are going to use the slope formula,
`m=(y_(2)-y_(1))/(x_(2)-x_(1))`, to find the slope of the line passing throughout our two points; then, we are going to replace the values in the point slope formula,
`y=m(x-x_(1))+y_(1)`, and simplify to complete the equation of our line.

Let's check this out with an example:

suppose you have the points (1,5) and (3,8), so
`x_(1)=1`,
`y_(1)=5`,
`x_(2)=3`, and
`y_(2)=8`.

First, we are going to use the slope formula to find the slope of the line passing throughout our two points:

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

`m=(8-5)/(3-1)`

`m=(3)/(2)`

Now that we have the slope of our line, we can use the point slope formula to complete our line equation:

`y=m(x-x_(1))+y_(1)`

`y=(3)/(2)(x-1)+5`

`y=(3)/(2) x-(3)/(2) +5`

`y=(3)/(2) x+(7)/(2)`