Question

What is an equation of the line that passes through the points left bracket, 3, comma, 3, right bracket(3,3) and left bracket, 3, comma, minus, 3, right bracket(3,−3)?

Answer 1

To find the equation of a line passing through two given points, we can use the slope-intercept form of a linear equation, which is given by:

y = mx + b

where m represents the slope of the line and b represents the y-intercept.

First, let's determine the slope (m) of the line passing through the points (3, 3) and (3, -3).

The formula to find the slope (m) between two points (x1, y1) and (x2, y2) is given by:

m = (y2 - y1) / (x2 - x1)

Using the coordinates, (x1, y1) = (3, 3) and (x2, y2) = (3, -3), we can substitute these values into the slope formula:

m = (-3 - 3) / (3 - 3)
m = -6 / 0

The slope is undefined because the denominator is zero, which implies that the line is vertical.

Since the line is vertical and passes through the x-coordinate 3, the equation of the line is simply x = 3.