Find an equation of the line passing through the given points. Write the equation in slope-intercept form, if possible.
$(5, 3)$ and $(5, - 8)^{2}$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Simplify your answer. Use integers or fractions for any numbers in the equation.)
A. The equation of the line in slope-intercept form is
B. The equation of the line cannot be written in slope-intercept form. The equation of the line is

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Answer

$x = 5$ is the final answer.

Steps

Step 1 ：The slope of a line passing through two points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ is given by the formula $\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ . However, if $x_{1} = x_{2}$ , the denominator of this fraction becomes zero, which means the slope is undefined. In this case, the line is vertical and cannot be written in slope-intercept form (which requires a defined slope). The equation of a vertical line is simply $x = x_{1}$ .

Step 2 ：In this case, the two points given are $(5, 3)$ and $(5, - 8)$ . Since the x-coordinates are the same, this is a vertical line and its equation is $x = 5$ .

Step 3 ： $x = 5$ is the final answer.

Answer

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