Answer:
[tex]y - 6 = -2(x-1)[/tex]
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
[tex](x_1, y_1) = (1,6)\\(x_2, y_2) = (3,2)[/tex]
The slope of a line is define as thus;
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{2 - 6}{3 - 1}[/tex]
[tex]m = \frac{-4}{2}[/tex]
[tex]m = -2[/tex]
Considering only point [tex](x_1, y_1) = (1,6)[/tex]; The slope is define as thus
[tex]m = \frac{y - y_1}{x - x_1}[/tex]
Substitute [tex]m = -2[/tex] and [tex](x_1, y_1) = (1,6)[/tex]
[tex]-2 = \frac{y - 6}{x - 1}[/tex]
Multiply both sides by x - 1
[tex]-2(x-1) = \frac{y - 6}{x - 1} (x-1)[/tex]
[tex]-2(x-1) = y - 6[/tex]
Rearrange
[tex]y - 6 = -2(x-1)[/tex]
Hence, the equation of the line is a point slope form is [tex]y - 6 = -2(x-1)[/tex]
