Question

graph the line that passes through the points (9,4) and (9,1) and determine the equation of the line.

Explanation:

Step1: Recall line - equation form

The general form of a line is $y - y_1=m(x - x_1)$ where $m=\frac{y_2 - y_1}{x_2 - x_1}$ for two points $(x_1,y_1)$ and $(x_2,y_2)$.

Step2: Calculate the slope

Let $(x_1,y_1)=(9,4)$ and $(x_2,y_2)=(9,1)$. Then $m=\frac{1 - 4}{9 - 9}=\frac{-3}{0}$, which is undefined.

Step3: Determine the line - equation

Since the $x$ - coordinates of the two points $(9,4)$ and $(9,1)$ are the same, the equation of the line is $x = 9$.

Step4: Graph the line

On the coordinate - plane, mark the points $(9,4)$ and $(9,1)$. Then draw a vertical line passing through these two points. The vertical line intersects the $x$ - axis at $x = 9$.

Answer:

The equation of the line is $x = 9$.