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:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

Substitute:

$m=\dfrac{3-2}{4-2}=\dfrac{1}{2}$

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:

$m=\dfrac{-1-2}{x-2}=\dfrac{-3}{x-2}$

We have the equation:

$\dfrac{-3}{x-2}=\dfrac{1}{2}$        cross multiply

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

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

$x=-4$

Answer: x = -4.