Question

What method can be used to write the equation of a line in slope-intercept form given two points?

Answer 1

Slope intercept form is : y = mx + b
where m is the slope and b is the y-intercept.

The slope, m = (y' - y)/(x' - x)
Is found using the two pints.
The apostrophe is used to denote the other point, different from point (x,y).

once you have the slope, m for the equation y = mx + b ; use one of the points as (x,y) to solve for b.

Answer 2

Answer:

$\frac{y_2-y_1}{x_2-x_1}$ is slope and $(y_1-\frac{y_2-y_1}{x_2-x_1}\,x_1)$ is y-intercept of line.

Step-by-step explanation:

Let the given two points are $(x_1,y_1)\:and\:(x_2,y_2)$

First we find the equation using two point form then rewrite in Slope intercept form.

Equation of line using two piont form,

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

$y-y_1=\frac{y_2-y_1}{x_2-x_1}\,x-\frac{y_2-y_1}{x_2-x_1}\,x_1$

$y=\frac{y_2-y_1}{x_2-x_1}\,x-\frac{y_2-y_1}{x_2-x_1}\,x_1+y_1$

$y=\frac{y_2-y_1}{x_2-x_1}\,x+(y_1-\frac{y_2-y_1}{x_2-x_1}\,x_1)$

here, $\frac{y_2-y_1}{x_2-x_1}$ is slope and $(y_1-\frac{y_2-y_1}{x_2-x_1}\,x_1)$ is y-intercept of line.