Question

G.1.- Una Recta contiene los puntos (-3,7)

y (9,-5) Calcule la ecuación de la recta en la
FORma y=mxtb. Explicar los pasos

Answer 1

Given:

A line passes through the points (-3,7) and (9,-5).

To find:

The equation of the line in the form of
`y=mx+b`.

Solution:

If a line passes through two points, then the equation of the line is:

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

A line passes through the points (-3,7) and (9,-5). So, the equation of the given line is:

`y-7=(-5-7)/(9-(-3))(x-(-3))`

`y-7=(-5-7)/(9+3)(x+3)`

`y-7=(-12)/(12)(x+3)`

`y-7=-1(x+3)`

On further simplification, we get

`y-7=-x-3`

`y-7+7=-x-3+7`

`y=-x+4`

Therefore, the equation of the required line is
`y=-x+4`.