Question

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

Answer 1

Answer:

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

Step-by-step 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;

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{2 - 6}{3 - 1}$

$m = \frac{-4}{2}$

$m = -2$

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

$m = \frac{y - y_1}{x - x_1}$

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

$-2 = \frac{y - 6}{x - 1}$

Multiply both sides by x - 1

$-2(x-1) = \frac{y - 6}{x - 1} (x-1)$

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

Rearrange

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

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