Question

Line a is parallel to line bLine a passes through the points (1,3) and (2,-8)Line b passes through the point (6,14)What is the equation of line b y=______

Answer 1

y=-11x+80

Step-by-step 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).

`\begin{gathered} \text{Slope},m_1=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}} \\ =(-8-3)/(2-1) \\ =-(11)/(1) \\ m_1=-11 \end{gathered}`

Step 2: Find the slope, m2 of line b.

Since the two lines are parallel:

`m_1=m_2=-11`

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:

`\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}`

The equation of line b is y=-11x+80.