Question

Which of the following point-slope form equations could be produced with the points (4, 5) and (-3, -5)?

Answer 1

Given:

The two points are (4,5) and (-3,-5).

To find:

The point-slope form equations could be produced with the given points.

Solution:

Slope formula:

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

The two points are (4,5) and (-3,-5). So, the slope of the line is:

`m=(-5-5)/(-3-4)`

`m=(-10)/(-7)`

`m=(10)/(7)`

The point slope form of a line is:

`y-y_1=m(x-x_1)`

Where, m is the slope of the line.

The slope of the line is
`m=(10)/(7)` is passes through the point (4,5). So, the point slope form is:

`y-5=(10)/(7)(x-4)`

The slope of the line is
`m=(10)/(7)` is passes through the point (-3,-5). So, the point slope form is:

`y-(-5)=(10)/(7)(x-(-3))`

`y+5=(10)/(7)(x+3)`

Therefore, the point slope form of the given line is either
`y-5=(10)/(7)(x-4)` or
`y+5=(10)/(7)(x+3)`.