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=(y_2-y_1)/(x_2-x_1)(x-x_1)`

`y-10=(-5-10)/(3-2)(x-2)`

`y-10=(-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`.