Question

A line passes through `(9 ,3 )` and `( 3, 5 )`. A second line passes through `( 7, 8 )`. What is one other point that the second line may pass through if it is parallel to the first line?

Answer 1

`(0, 17)`

Explanation:

Parallel lines have the same slope.

Get the slope using the points passed through by the first line

`m = (y_1 - y_2)/(x_1 - x_2)`

`P_1: (9, 3)`
`P_2: (3, 5)`

`=> m = (3 - 5)/(9 - 3)`

`=> m = -2/6 = -1/3`

---

Get the equation of the second line

`y = mx + b`

`y = -1/3x + b`

Substitute the point passed through by the second line to get the y-intercept

`P_1': (7, 8)`

`8 = -1/3(7) + b`

`24 = -7 + b`

`b = 17`

Hence, the equation of the second line is

`y = -1/3x + 17`

---

To determine another point that the line passes through, simply select a desired value for either `x` or `y`. Substitute the desired value into the equation to get its corresponding `y` (or `x`).

For simplicity, let's use `x = 0`.

`y = -1/3(0) + 17`

`y = 17`

Hence, we have

`P_2': (0, 17)`