Draw a straight line that passes through the points (3, 4) and (-3, 4). Is the graph of (0, 4) on this line?

Question

Quizplus · Accepted Answer

The equation of the line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by
$$\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}.$$
Substituting $(x_1,y_1)=(3,4)$ and $(x_2,y_2)=(-3,4)$ in the above equation, we get
$$\frac{y-4}{x-3}=\frac{0}{-6}\implies x-3=0\implies x=3.$$
Thus, the equation of the line is $x=3,$ which is a vertical line passing through $(3,4)$ and $(-3,4).$ Since the $y$-coordinate of the point $(0,4)$ is also $4,$ it lies on this line.

Draw a Straight Line That Passes Through the Points (3