Question

write an equation in slope-intercept form of the line passing through the given pair of points. the line goes through the points (8,1) and (8,3). the equation of the line is \boxed{}. (simplify your answer. type your answer in slope-intercept form. use integers or fractions for any numbers in the equation.)

Explanation:

Step1: Calculate the slope

The slope formula is $m=\frac{y_2-y_1}{x_2-x_1}$. For points $(8,1)$ and $(8,3)$:
$m=\frac{3-1}{8-8}=\frac{2}{0}$, which is undefined. This means the line is vertical.

Step2: Identify vertical line equation

Vertical lines have the form $x=a$, where $a$ is the constant x-value of all points on the line. Here, $x=8$ for both points.

Step3: Note slope-intercept limitation

Slope-intercept form is $y=mx+b$, but vertical lines cannot be written in this form because their slope is undefined. However, the only equation describing this line is $x=8$.

Answer:

$x=8$