y=-11x+80
Explanation:
Two lines are said to be parallel if they have the same slope.
Step 1: Find the slope of line a.
Line a passes through the points (1,3) and (2,-8).
[tex]\begin{gathered} \text{Slope},m_1=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}} \\ =\frac{-8-3}{2-1} \\ =-\frac{11}{1} \\ m_1=-11 \end{gathered}[/tex]Step 2: Find the slope, m2 of line b.
Since the two lines are parallel:
[tex]m_1=m_2=-11[/tex]Step 3: Find the equation of line b.
Line b passes through the point (x1,y1)=(6,14) and has a slope, m=-11.
Using the point-slope form of the equation of a line:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-14=-11(x-6) \\ y-14=-11x+66 \\ y=-11x+66+14 \\ y=-11x+80 \end{gathered}[/tex]The equation of line b is y=-11x+80.
