To solve this problem you must apply the proccedure shown below:
1- You have that the equation of the line is:
[tex] y=mx+b [/tex]
Where [tex] m [/tex] is the slope and[tex] b [/tex] is the y-intercept.
2- Based on the information given in the problem, the lines [tex] AB [/tex] and[tex] CD [/tex] are parallel, which means that both have the same slope. Therefore, you can calculate the slope of [tex] AB [/tex]:
[tex] m=\frac{y2-y1}{x2-x1} [/tex]
[tex] m=\frac{4-1}{1-(-6)}=\frac{3}{7} [/tex]
3- Use the coordinates of the point [tex] D(7,2) [/tex] to calculate the y-intercept:
[tex] 2=\frac{3}{7}(7)+b [/tex]
4. Solve for [tex] b [/tex]:
[tex] b=2-3=-1 [/tex]
5. The equation of the line [tex] CD [/tex] is:
[tex] y=\frac{3}{7}x-1 [/tex]
The answer is: [tex] y=\frac{3}{7}x-1 [/tex]
