Write the equation of the line that passes through the points left bracket, minus, 1, comma, 4, right bracket ( − 1 , 4 ) (−1,4) and left bracket, minus, 1, comma, 0, right bracket ( − 1 , 0 ) (−1,0). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
Since both points have the same x-coordinate of -1, the line is a vertical line. The equation of a vertical line in point-slope form is x = a, where a is the x-coordinate of any point on the line. Therefore, the equation of the line passing through (-1,4) and (-1,0) is x = -1.
To find the equation of the line passing through the points (-1, 4) and (-1, 0), we need to determine the slope of the line and one of the points.
The slope (m) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Using the coordinates (-1, 4) for (x1, y1) and (-1, 0) for (x2, y2), we have:
m = (0 - 4) / (-1 - (-1))
m = -4 / 0
m = undefined
Since the slope is undefined, it means the line is vertical.
Therefore, the equation of the line passing through the points (-1, 4) and (-1, 0) is x = -1.