For this case we have that by definition, the equation of a line in the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cutoff point with the y axis
[tex]m = \frac {y2-y1} {x2-x1}[/tex]
We have the following points:[tex](x1, y1) :( 5,6)\\(x2, y2) :( 4,8)[/tex]
Substituting:
[tex]m = \frac {8-6} {4-5}\\m = \frac {2} {- 1}\\m = -2[/tex]
Then, the equation is:
[tex]y = -2x + b[/tex]
To find "b" we substitute one of the points:
[tex]8 = -2 (4) + b\\8 = -8 + b\\b = 8 + 8\\b = 16[/tex]
Finally, the equation is:
[tex]y = -2x + 16[/tex]
Answer:
Option B
