Question

I Point

Which of the following is a point-slope equation of a line that passes through
the points (5, 2) and (-1, -6)?
Α. y-2 = (x-5)
Β. y-2--3-5)
C. y-2-3 (x-5)
D. y-2--5)

Answer 1

The equation of line is
`(y-2) = (4)/(3) (x -5)`

Explanation:

Here, the two point line are given as is A(5,2) and B(-1,-6)

The slope of the line AB =
`m = (y_2 - y_1)/(x_2 - x_1)`

`= (-6- 2)/(-1 -5)  = (-8)/(-6)  = (4)/(3)`

⇒ the slope of AB is m = (4/3)

By POINT SLOPE FORMULA:

The equation of a line with slope m and a point (x0, y0) is given as

(y-y0)= m (x-x0)

⇒ The equation of line with point (5,2) is:

`(y-2) = (4)/(3) (x -5)`

Hence, the equation of line is
`(y-2) = (4)/(3) (x -5)`