Question

vertical lines
what is the equation of the line that passes through the points (2, -3) and (2, 6)?

1. find the slope of the line.

m =

1. does a vertical line have a y-intercept?

1. write the equation of the line.

Explanation:

Sub - Question 1: Find the slope of the line.

Step 1: Recall the slope formula

The slope \( m \) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
Here, \( x_1 = 2,y_1=-3,x_2 = 2,y_2 = 6 \).

Step 2: Substitute the values into the formula

Substituting the values, we get \( m=\frac{6-(-3)}{2 - 2}=\frac{6 + 3}{0}=\frac{9}{0} \). Division by zero is undefined, so the slope is undefined.

A vertical line has the equation \( x = a \) (where \( a \) is a constant). A y - intercept is a point where \( x = 0 \). For a vertical line \( x=a \), if \( a
eq0 \), there is no point where \( x = 0 \), and if \( a = 0 \), the line is the y - axis itself. But in general, a vertical line (except the y - axis) does not have a y - intercept, and the concept of a y - intercept is not applicable in the usual sense for a vertical line as it is parallel to the y - axis (or is the y - axis). So the answer is no.

Step 1: Recall the equation of a vertical line

A vertical line passing through a point \((a,b)\) has the equation \( x=a \).

Step 2: Identify the x - coordinate of the given points

The given points are \((2,-3)\) and \((2,6)\). The x - coordinate of both points is 2.

Answer:

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Sub - Question 2: Does a vertical line have a y - intercept?