A line with slope m and that passes through the point (x₁, y₁) have the following point-slope form equation:
[tex]y-y_1=m(x-x_1)[/tex]
Furthermore, if this line passes through a second point (x₂, y₂), its slope is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
In this problem, the given line passes through points (6, 2) and (10, -1). So, we have:
x₁ = 6
y₁ = 2
x₂ = 10
y₂ = -1
Then, using those values to find m, we obtain:
[tex]m=\frac{-1-2}{10-6}=-\frac{3}{4}[/tex]
And the equation of the line, in point-slope form, is:
[tex]y-2=-\frac{3}{4}(x-6_{})[/tex]
Therefore, option A is correct.
