Question

The points with coordinates (x, -1), (2,2), and (4,3) lie on the same line. What is the value of x?

Answer 1

Find the slope of the line passing throught the points (2, 2) and (4, 3).

The formula of a slope:

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

Substitute:

`m=(3-2)/(4-2)=(1)/(2)`

If the point (x, -1) lie on the same line, then the slope of line passing through the points (2, 2) and (x, -1) the same:

Substitute:

`m=(-1-2)/(x-2)=(-3)/(x-2)`

We have the equation:

`(-3)/(x-2)=(1)/(2)` cross multiply

`(1)(x-2)=(-3)(2)`

`x-2=-6` add 2 to both sides

`x=-4`

Answer: x = -4.