Answer:
[tex]y=\frac{1}{4} x+3.[/tex]
Step-by-step explanation:
1. if the points (-4;2) and (12;6) belong to the required line, then it is possible to make up its equation:
[tex]\frac{x+4}{12+4} =\frac{y-2}{6-2}; \ \frac{x+4}{4}=\frac{y-2}{1};[/tex]
2. if the common form of line in slope-interception form is 'y=s*x+i' (where s - slope, i - interception), then after evaluation of the equation in item 1:
4(y-2)=x+4; ⇒ 4y=x+12; ⇔
[tex]y=\frac{1}{4}x+3.[/tex]
