Question

Line AB contains points A(-6,1) and B(1,4).

Answer 1

To solve this problem you must apply the proccedure shown below:

1- You have that the equation of the line is:

$y=mx+b$

Where $m$ is the slope and$b$ is the y-intercept.

2- Based on the information given in the problem, the lines $AB$ and$CD$ are parallel, which means that both have the same slope. Therefore, you can calculate the slope of $AB$:

$m=\frac{y2-y1}{x2-x1}$

$m=\frac{4-1}{1-(-6)}=\frac{3}{7}$

3- Use the coordinates of the point $D(7,2)$ to calculate the y-intercept:

$2=\frac{3}{7}(7)+b$

4. Solve for $b$:

$b=2-3=-1$

5. The equation of the line $CD$ is:

$y=\frac{3}{7}x-1$

The answer is: $y=\frac{3}{7}x-1$