Question

Write the equation for a line in Slope-Intercept Form (y = mx +b) given the two points below (2,10) (3,-5)

Answer 1

Given:

The two end points of a line are (2,10) and (3,-5).

To find:

The equation of the line in the slope intercept form.

Solution:

The slope intercept form of a line is

$y=mx+b$

Where, m is slope and b is the y-intercept.

The two end points of a line are (2,10) and (3,-5). So, the equation of the line is

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

$y-10=\dfrac{-5-10}{3-2}(x-2)$

$y-10=\dfrac{-15}{1}(x-2)$

$y-10=-15(x-2)$

On further simplification, we get

$y-10=-15x+30$

$y=-15x+30+10$

$y=-15x+40$

Therefore, the slope intercept form of the given line is $y=-15x+40$.