Question

Which equation is a point slope form equation for line AB?

Oy+2 = -2(3-5)
А
Oy+6= -2(x - 1)
Oy+1=-2 (3-6)
Oy+5 = -2(3-2)

Answer 1

`y - 6 = -2(x-1)`

Explanation:

Given; The graph above

Required: Equation of line AB (in point slope form)

First, we need to determine the slope of the graph;

From the graph; we can observe that when y = 6, x = 1 and when y = 2, x = 3

Such that

`(x_1, y_1) = (1,6)\\(x_2, y_2) = (3,2)`

The slope of a line is define as thus;

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

`m = (2 - 6)/(3 - 1)`

`m = (-4)/(2)`

`m = -2`

Considering only point
`(x_1, y_1) = (1,6)`; The slope is define as thus

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

Substitute
`m = -2` and
`(x_1, y_1) = (1,6)`

`-2 = (y - 6)/(x - 1)`

Multiply both sides by x - 1

`-2(x-1) = (y - 6)/(x - 1) (x-1)`

`-2(x-1) = y - 6`

Rearrange

`y - 6 = -2(x-1)`

Hence, the equation of the line is a point slope form is
`y - 6 = -2(x-1)`