For this case we have that the equation of a line of the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cut-off point with the y axis
[tex]m = \frac {y2-y1} {x2-x1}[/tex]
We have the following points:
[tex](x1, y1): (7,2)\\(x2, y2): (2,12)[/tex]
Substituting:
[tex]m = \frac {12-2} {2-7} = \frac {10} {- 5} = - 2[/tex]
Thus, the equation is of the form:
[tex]y = -2x + b[/tex]
We substitute one of the points to find the cut point "b":
[tex]2 = -2 (7) + b\\2 = -14 + b\\2 + 14 = b\\16 = b[/tex]
Thus, the equation is:
[tex]y = -2x + 16[/tex]
Answer:
[tex]y = -2x + 16[/tex]
