ANSWER
A. y = -1/4x + 10
EXPLANATION
We have to find the equation of the line in slope-intercept form,
[tex]y=mx+b[/tex]
Where m is the slope and b is the y-intercept.
The slope of a line passing through points (x₁, y₁) and (x₂, y₂) is,
[tex]m=\frac{y_1-y_2}{x_1-x_2}[/tex]
In this case, only two points are given, so the slope of the line is,
[tex]m=\frac{6-9}{16-4}=\frac{-3}{12}=-\frac{1}{4}[/tex]
So, for now, the equation is,
[tex]y=-\frac{1}{4}x+b[/tex]
To find the y-intercept, b, replace x and y with one of the points,
[tex]9=-\frac{1}{4}(4)+b[/tex]
And solve for b,
[tex]9=-1+b\text{ }\Rightarrow\text{ }b=9+1=10[/tex]
Hence, the equation of the line is y = -1/4x + 10.
