Question

Choose all the lines that are parallel to the line pictures in the graph below

Answer 1

Two lines are parallel if they have the same slope

Given two points (x1, y1) and (x2, y2) of the line, its slope (m) is computed as follows:

`m\text{ = }(y_2-y_1)/(x_2-x_1)`

From the picture, points (0,-2) and (2, -3) lie on the line. Then, its slope is:

`m\text{ =}\frac{-3\text{ - (}-2)}{2\text{ - 0}}=(-1)/(2)`

Then, the first and fifth options are parallel to the line in the picture.

From the case: 2y = -x - 4, we have to isolate y, as follows:

y = (-x - 4)/2

y = -1/2 x - 4/2

y = -1/2 x - 2

Therefore, this line is parallel too.

From the case: x + 2y = 8, we have to isolate y, as follows:

2y = 8 - x

y = (8 - x)/2

y = 8/2 - 1/2 x

y = 4 - 1/2 x

Therefore, this line is parallel too.