Question

The coordinates of 3 of the vertices of a parallelogram are (–7, 3), (–6, 1), and (–4, 5). What is the equation for the line containing the side opposite the side containing the first two vertices? (Remember, opposite sides of a parallelogram are parallel.)

Answer 1

Answer:
`y=-2x-3`

Explanation:

The equation of the line in slope-intercept form, is:

`y=mx+b`

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

By definition, parallel lines have the same slope.

Then:

- Find the slope of the the line that connects the points (-7,3) and (-6,1), as following:

`m=(y_2-y_1)/(x_2-x_1)\\\\m=(1-3)/(-6-(-7))=-2`

- We know that the other line is connected with the point (-4,5), therefore, you can substitute values and solve for b:

`5=-2(-4)+b\\5=8+b\\5-8=b\\b=-3`

Then, the equation for the line containing the side opposite the side containing the first two vertices is:

`y=-2x-3`